Example Question - supplementary angles
Here are examples of questions we've helped users solve.
Angle Relationship Problem
Так как данный вопрос содержит математическую задачу, я приступлю к её решению. <p>Для того чтобы решить данную задачу, необходимо использовать свойства смежных углов и свойства углов, образованных при пересечении двух прямых секущей.</p> <p>По условию задачи нам известны углы \( \angle 1 \), \( \angle 2 \), и требуется найти угол \( \angle 3 \).</p> <p>Смежные углы в сумме составляют \( 180^\circ \), следовательно, если углы \( \angle 1 \) и \( \angle 3 \) смежные, то:</p> <p>\[ \angle 3 = 180^\circ - \angle 1 \]</p> <p>Из условия задачи известно, что \( \angle 1 \) равен \( 117^\circ \), следовательно:</p> <p>\[ \angle 3 = 180^\circ - 117^\circ = 63^\circ \]</p> <p>Чтобы найти угол \( \angle 2 \), нужно использовать свойство вертикальных углов, которые равны между собой. Углы \( \angle 2 \) и \( \angle 1 \) являются вертикальными, следовательно:</p> <p>\[ \angle 2 = \angle 1 = 117^\circ \]</p> <p>Таким образом, угол \( \angle 3 \) равен \( 63^\circ \), а угол \( \angle 2 \) равен \( 117^\circ \).</p>
Solving for Angular Measures of Veins in a Leaf
The problem states that the veins in a leaf form a pair of supplementary angles. Supplementary angles are two angles whose measures add up to 180 degrees. It gives us the measures of the two angles in terms of x: \( m\angle1 = 7x + 13^\circ \) \( m\angle2 = 25x + 7^\circ \) Because they are supplementary, we can set up the following equation to solve for x: \( 7x + 13^\circ + 25x + 7^\circ = 180^\circ \) Combine like terms: \( 32x + 20^\circ = 180^\circ \) Subtract 20 degrees from both sides to isolate the terms with x: \( 32x = 160^\circ \) Divide both sides by 32 to find x: \( x = 160^\circ / 32 = 5^\circ \) Now that we know the value of x, we can substitute it into the expressions for the angles to find their measures: \( m\angle1 = 7(5^\circ) + 13^\circ = 35^\circ + 13^\circ = 48^\circ \) \( m\angle2 = 25(5^\circ) + 7^\circ = 125^\circ + 7^\circ = 132^\circ \) Therefore, the measures of the angles are 48 degrees and 132 degrees, respectively.
Finding Supplementary Angles in Leaf Veins
The question states that the veins in a leaf form a pair of supplementary angles. Supplementary angles are two angles whose measures add up to 180 degrees. Given the measures of the two angles as \( m\angle1 = (7x + 13)^\circ \) and \( m\angle2 = (25x + 7)^\circ \), we can set up an equation that reflects their supplementary nature: \[ (7x + 13) + (25x + 7) = 180 \] Simplify the equation: \[ 7x + 25x + 13 + 7 = 180 \] \[ 32x + 20 = 180 \] Now, solve for \( x \): \[ 32x = 180 - 20 \] \[ 32x = 160 \] \[ x = \frac{160}{32} \] \[ x = 5 \] Now that we have the value of \( x \), we can find the measure of each angle: \[ m\angle1 = 7x + 13 \] \[ m\angle1 = 7(5) + 13 \] \[ m\angle1 = 35 + 13 \] \[ m\angle1 = 48^\circ \] And for the other angle: \[ m\angle2 = 25x + 7 \] \[ m\angle2 = 25(5) + 7 \] \[ m\angle2 = 125 + 7 \] \[ m\angle2 = 132^\circ \] So the measures of the two angles are 48 degrees and 132 degrees, respectively.
Finding the Measure of Angle WYX in a Rhombus
The image shows a geometric figure labeled WXYZ, which is identified as a rhombus. There is an angle at vertex Y that is marked as 75 degrees. The question asks for the measure of the angle ∠WYX. In a rhombus, opposite angles are equal and adjacent angles are supplementary (meaning they add up to 180 degrees). Since the angle at vertex Y is given as 75 degrees, the angle at vertex W (which is adjacent to angle Y) would be supplementary to it. Therefore, to find the measure of angle W (∠WYX), we need to subtract the angle at vertex Y from 180 degrees: ∠WYX = 180 degrees - ∠Y = 180 degrees - 75 degrees = 105 degrees So the measure of angle ∠WYX is 105 degrees.
Solving for Angles in a Kite Figure
From the image provided, it appears to be a problem involving a geometric figure, specifically a kite. In the kite, there are two angles labeled \(52^\circ\) and \(60^\circ\) and two unknown angles labeled \(x\) and \(y\). To solve for x and y, we can use the fact that the adjacent angles between the unequal sides of a kite are supplementary (they add up to 180 degrees), and the fact that the sum of all angles in a quadrilateral is 360 degrees. Let's denote the angles of the kite by A, B, C, and D, starting from the \(52^\circ\) angle and going counterclockwise, so: - A = \(52^\circ\) (given) - B = \(x^\circ\) (unknown) - C = \(60^\circ\) (given) - D = \(y^\circ\) (unknown) Because A and B are adjacent between the unequal sides: A + B = \(180^\circ\) \(52^\circ + x^\circ = 180^\circ\) \(x^\circ = 180^\circ - 52^\circ\) \(x^\circ = 128^\circ\) And since C and D are also adjacent between the unequal sides: C + D = \(180^\circ\) \(60^\circ + y^\circ = 180^\circ\) \(y^\circ = 180^\circ - 60^\circ\) \(y^\circ = 120^\circ\) So the values of x and y would be: \(x = 128^\circ\) \(y = 120^\circ\)
Geometric Figure Angle Calculation
The image shows a geometric figure involving a parallelogram JKNL with one of the interior angles labeled as 50 degrees (angle J) and two transversals JL and KN intersecting inside the parallelogram, forming several angles with algebraic expressions: 4z + 88 (angle KJL), 2z + 68 (angle LKN), and 45 degrees (angle JKN). In a parallelogram, opposite angles are equal, so angle J (50 degrees) is equal to angle L. Also, consecutive angles in a parallelogram are supplementary, meaning they add up to 180 degrees. Therefore, angle K and angle J must add up to 180 degrees. Since angle J is 50 degrees, angle K is 180 - 50 = 130 degrees. Angle M (angle JKN) is given as 45 degrees. Since KN is a straight line, angles KJL and JKN add up to 180 degrees because they are supplementary. Thus, we can set up the equation: 4z + 88 + 45 = 180. Now we can solve for z: 4z + 88 + 45 = 180 4z + 133 = 180 4z = 180 - 133 4z = 47 z = 47 / 4 z = 11.75 So, the value of x is 11.75.
Solving Geometry Problem with Intersecting Chords Theorem
This geometry problem involves a circle with two intersecting chords. According to the intersecting chords theorem (sometimes called the chord-chord product theorem), opposite angles formed by two intersecting chords are supplementary. This means that their sum is 180 degrees. In the provided image, you have two angles labeled x° and y°, along with two given angles of 46° and 90°. According to the theorem: x° + 46° = 180° (since they are opposite angles) y° + 90° = 180° (since they are opposite angles) Let's solve for x and y: x° = 180° - 46° x° = 134° For y: y° = 180° - 90° y° = 90° Therefore, the values of x and y are: x = 134° y = 90°
Geometry Angle Problems Solution
The image displays two geometry problems, with accompanying figures, asking to find the measures of the marked angles. For the first problem (A): 1. m∠ACD = (4x + 8)° 2. m∠ACB = (2x)° To solve for x, use the fact that ∠ACB and ∠ACD are supplementary angles (since they form a straight line together), so their measures add up to 180 degrees: (4x + 8)° + (2x)° = 180° 6x + 8 = 180 6x = 172 x = 28.67° (approximately) Now you can find the measure of ∠ACD using the value of x: m∠ACD = (4x + 8)° = (4*28.67 + 8)° = 122.67° (approximately) For the second problem (B): 1. m∠BCD = (3x + 11)° 2. m∠ACD = (5x)° Again, ∠BCD and ∠ACD are supplementary angles, so their total measure is 180 degrees: (3x + 11)° + (5x)° = 180° 8x + 11 = 180 8x = 169 x = 21.125° (approximately) Now you can find the measure of ∠ACD: m∠ACD = (5x)° = (5*21.125)° = 105.625° (approximately) So, for each problem, we have found the measures of the respective marked angles using the properties of supplementary angles.
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