Example Question - interior angles
Here are examples of questions we've helped users solve.
Triangle Angle Calculation Problem
<p>Let the angles of the triangle be A, B, and C.</p> <p>Given: A = 50 degrees, B = 60 degrees.</p> <p>The sum of the angles in a triangle is always 180 degrees.</p> <p>A + B + C = 180 degrees</p> <p>50 degrees + 60 degrees + C = 180 degrees</p> <p>110 degrees + C = 180 degrees</p> <p>C = 180 degrees - 110 degrees</p> <p>C = 70 degrees</p>
Finding the Value of an Angle in a Kite-like Figure
\begin{align*} m\angle EAD + m\angle ADC + m\angle DAB &= 180^\circ \quad \text{(Sum of interior angles of $\triangle ADB$)} \\ x + 118^\circ + 30^\circ &= 180^\circ \\ x + 148^\circ &= 180^\circ \\ x &= 180^\circ - 148^\circ \\ x &= 32^\circ \end{align*}
Geometric Problem Involving Polygons and Angles
Bu geometri problemi, çokgenler ve iç açılarla ilgili. Verilen bilgilere göre, ABCDEF düzgün altıgen olduğundan, tüm iç açıları eşit ve her biri 120 derecedir (düzgün bir çokgenin her iç açısı (n-2)*180/n formülü ile bulunur, burada n kenar sayısıdır; altıgen için n=6). IPF | EF olduğu belirtilmiş, yani IPF ve EF doğru parçaları birbirine paralel. Bu durumda, PEF açısı E köşesindeki iç açı ile aynı ölçüde olacaktır çünkü paralel kenarlar ve transversallerle oluşan iç ters açılardır. Bu nedenle, m(PEF) açısının ölçüsü de 120 derecedir. Fakat sorulan m(PEF) değil, m(EF) açısıdır. Eğer EF, altıgenin iç açısına komşu bir dış açı ise, dış açı ve iç açının toplamı 180 derece olmalıdır çünkü bir doğru üzerinde komşu açılar oluştururlar ve bu durumda m(EF) = 180 - m(PEF) = 180 - 120 = 60 derece olur. Ancak soru bu değeri değil, bu komşu olmayan dış açının ölçüsünü istemektedir. m(FAP) = 35 derece verildiği için ve bu açı da EF ile aynı doğru üzerinde olduğu için, açılar toplamı 180 derece olacaktır. O zaman: m(EF) + m(FAP) = 180 m(EF) + 35 = 180 m(EF) = 180 - 35 m(EF) = 145 derece olur. Ancak soruda m(EF) değil, gerçekte m(PEF) sorulmuştur ve yukarıda belirttiğimiz gibi bu değer 120 derecedir. Yanıt olarak yanlış soruyu çözdüm, aslen m(PEF) sorulmuş ve bu açı 120 derecedir fakat şıklarda bu değer yok. Şıklarda yanlışlık olabileceğini düşünüyorum ya da sorunun orijinalinde bir hata var. Sorunun yeniden gözden geçirilmesi gerekebilir. Ancak verilen bilgiler çerçevesinde, m(PEF) kesinlikle 120 derece olur.
Solving Triangle Angles with 'x' Degrees
The image shows a triangle with angles labeled in terms of 'x'. To solve for 'x', we'll use the fact that the sum of the interior angles of any triangle is always 180 degrees. The angles are labeled as follows: - One angle is x degrees. - The second angle is 4x + 50 degrees. - The third angle is 3x - 10 degrees. Let's write an equation that sums these angles to 180 degrees: x + (4x + 50) + (3x - 10) = 180 Now, we can simplify and solve for 'x': x + 4x + 50 + 3x - 10 = 180 8x + 40 = 180 8x = 180 - 40 8x = 140 x = 140 / 8 x = 17.5 Therefore, 'x' is 17.5 degrees.
Deduction of Angles in a Star-shaped Figure
The image shows two geometric diagrams. However, the second diagram with the question "Find the sum of angle a and angle b" is the relevant part here. The image is a bit blurry, but I will attempt to help you with the information visible. From the diagram, it appears to be a star-shaped figure, suggesting that angle a and angle b are interior angles of a pentagon inscribed in the star. When multiple triangles are radiating from a central point, this implies the sum of the angles at the central point is 360 degrees due to the circular arrangement. It isn't evident from the diagram whether there are any special properties, such as equal sides or angles, that we could use directly. Yet, if we consider a regular pentagon (since it appears all sides may be equal), then the sum of the interior angles of any polygon can be calculated using the formula: Sum of interior angles = (n - 2) * 180 degrees Where n is the number of sides. For a pentagon (n=5), the sum of its interior angles is: Sum = (5-2) * 180 = 3 * 180 = 540 degrees Since a regular pentagon has all angles equal, each angle is: Each angle = 540 degrees / 5 = 108 degrees However, the sum of angles a and b, as exhibited in the star figure, appears to be less straightforward than simply adding two angles of a regular pentagon because these angles are formed by the intersection of the extensions of the sides of the pentagon. Angle a seems to be an external angle of the pentagon, and since the external angles of a polygon add up to 360 degrees, angle a would be Angle a = 360 degrees / 5 = 72 degrees (if the pentagon is regular). Angle b is an internal angle of the overlapping triangles. Without additional information on the relationships between the angles in the figure, we cannot definitively calculate the value of angle b. To accurately determine the sum of angle a and angle b, I would need further details about the properties of the figure and clear visibility of any marked angles or sides. If any other angles or side lengths are given, they might help solve for angles a and b. Please provide additional information, such as whether the star is regular, and if there are any given angles or relationships stated in the problem.
Polygon Exterior Angles Sum Calculation
The image displays a math problem that states the following: "The sum of the measures of the interior angles of a polygon is equal to 1260° - 180°/n, where n is the number of sides of the polygon. What is the sum of the measures of the exterior angles of a polygon with twelve sides?" To solve this problem, we need to first understand a few key points: 1. The sum of the measures of the interior angles of a polygon with n sides is given by the formula (n-2) * 180°. 2. The measure of each exterior angle is supplementary to the measure of its corresponding interior angle, meaning they add up to 180°. 3. The sum of the measures of the exterior angles of any polygon is always 360°, regardless of the number of sides. At this point, we don't really need to compute the sum of the interior angles as provided in the question since the sum of the exterior angles is independent of the number of sides—the answer is always 360°. Therefore, the sum of the measures of the exterior angles of a polygon with 12 sides is: 360° Hence, the correct answer is option B) 360°.
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