Example Question - vertical angles
Here are examples of questions we've helped users solve.
Vertical Angles and Angle Equality
The image shows two lines that intersect each other forming an angle of 113°. The other angle labeled "x°" is the vertical angle to the 113° angle. Vertical angles, also known as vertically opposite angles, are pairs of opposite angles made by two intersecting lines. Vertical angles are always equal to one another. Thus, the angle marked "x°" is also equal to 113°.
Vertical Angles and Straight Line Angles Calculation
The image depicts two angles formed by a straight line and a vertically opposite angle, which are always equal. The two angles given are: 1. \((4x + 2)^\circ\) 2. \((7x - 6)^\circ\) Since they are vertically opposite angles, they are equal. Therefore, we can set up the following equation: \(4x + 2 = 7x - 6\) Now, let's solve for \(x\): \(4x + 2 = 7x - 6\) \(6 + 2 = 7x - 4x\) \(8 = 3x\) \(x = \frac{8}{3} \approx 2.67\) Now we can use the value of \(x\) to find \(y\). Looking at the lines, we can see that they form a straight line and the sum of angles on a straight line is \(180^\circ\). This information can be used to form an equation using either of the two expressions for the angles given: Using the angle \((4x + 2)^\circ\), we get: \(4x + 2 + y = 180\) Now substituting the value of \(x\) we found: \(4(\frac{8}{3}) + 2 + y = 180\) \( \frac{32}{3} + 2 + y = 180\) \( \frac{38}{3} + y = 180\) Multiply both sides by 3 to rid the fraction: \(38 + 3y = 540\) Now subtract 38 from both sides: \(3y = 540 - 38\) \(3y = 502\) Divide both sides by 3 to solve for \(y\): \(y = \frac{502}{3}\) \(y = 167.\overline{333}\) or \(167\frac{1}{3}^\circ\) Hence, the values are: \(x \approx 2.67\) \(y \approx 167.33^\circ\) or \(167\frac{1}{3}^\circ\)
Finding Angle Value with Intersecting Lines
The image shows two intersecting lines, with one angle labeled as 70 degrees. The question asks to find the value of "m," which seems to be the angle opposite the 70-degree angle. Since the lines are intersecting, the opposite angles, also known as vertical angles, are congruent. This means that the angle labeled "m" is also 70 degrees. Therefore, the value of m is 70 degrees.
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