Question

Find the missing angle measure in each triangle. Show your work.

a) ∠A = 90°, ∠B = 45°, ∠C = 45°
b) ∠A = 60°, ∠B = 60°, ∠C = 60°
c) ∠A = 90°, ∠B = 30°, ∠C = 60°
d) ∠A = 45°, ∠B = 45°, ∠C = 90°

Answer 1

To find the missing angle in each triangle, subtract the sum of the known angles from 180°. In triangles a) and b), the missing angles are both 45° and 60° respectively, forming isosceles right and equilateral triangles. Triangle c) has no missing angle, and triangle d) is a right-angled isosceles triangle with the missing angle being 90°.

Step-by-step explanation:

To find the missing angle measure in each triangle, we use the fact that the sum of angles in a triangle is always 180 degrees. Here's how to find the missing angles in the given triangles:

• Triangle a): We have angles ∠A = 90° and ∠B = 45°. The sum of the angles is currently 135° (90 + 45). To find ∠C, we subtract this sum from 180°: 180° - 135° = 45°. So, ∠C also equals 45°.
• Triangle b): We have angles ∠A = 60° and ∠B = 60°. The sum of these angles is 120°. Again, we subtract from 180° to find ∠C: 180° - 120° = 60°. So, ∠C equals 60° as well, forming an equilateral triangle.
• Triangle c): Apparently, the angles given are ∠A = 90°, ∠B = 30°, and ∠C = 60°, which already sum up to 180°. There is no missing angle since the provided angles are already compliant with the angle sum property of triangles.
• Triangle d): We have ∠A = 45° and ∠B = 45°. The sum of these angles is 90°. Subtracting from 180° to find ∠C, we get: 180° - 90° = 90°. Thus, ∠C equals 90°, resulting in a right-angled isosceles triangle.