Find unknown angles in any triangles - Reasoning

In this geometry exercise, students are tasked with finding the unknown angles labelled a, b, c, and d within a series of triangles, using the information provided. The given angles are 56 degrees and 87 degrees. To determine the size of angle a, students can rely on the principle that vertically opposite angles are equal, which means angle a is also 56 degrees. For angle d, they need to apply the rule that angles on a straight line add up to 180 degrees; therefore, angle d is calculated by subtracting 87 degrees from 180 degrees, resulting in 93 degrees.

The calculation of angle c involves understanding that the sum of angles in a triangle is always 180 degrees. Since angle a and angle d are part of a triangle and their values are known, students can use the formula a + d + c/2 = 180 degrees to find that angle c is 62 degrees. To find angle b, students subtract the sum of angles a and c from 180 degrees, which also results in 62 degrees. Upon reflection, students should notice that the large triangle in the problem is an isosceles triangle, indicated by the two angles b and c being equal. This exercise not only tests students’ ability to calculate unknown angles but also reinforces their understanding of the properties of different types of triangles.