Question

Find the missing angle measures. Remember not to assume right angles or diameters. Think about how many degrees are in a triangle.

a) 30°, 60°, 90°
b) 45°, 45°, 90°
c) 60°, 75°, 45°
d) 90°, 90°, 90°

Answer 1

To find the missing angle measures, we can use the fact that the sum of the angles in a triangle is always 180 degrees. By subtracting the given angles from 180 degrees, we can find the missing angles in each triangle.

Step-by-step explanation:

To find the missing angle measures, we need to keep in mind that the sum of the angles in a triangle is always 180 degrees.

(a) In the triangle with angles 30°, 60°, and the missing angle, we have 30° + 60° + x = 180°. Solving for x, we get x = 180° - 30° - 60° = 90°.

(b) In the triangle with angles 45°, 45°, and the missing angle, we have 45° + 45° + x = 180°. Solving for x, we get x = 180° - 45° - 45° = 90°.

(c) In the triangle with angles 60°, 75°, and the missing angle, we have 60° + 75° + x = 180°. Solving for x, we get x = 180° - 60° - 75° = 45°.

(d) In the triangle with angles 90°, 90°, and the missing angle, we have 90° + 90° + x = 180°. Solving for x, we get x = 180° - 90° - 90° = 0°.