Question

For exercises 1 and 2, find the unknown angle measures in each triangle.

option a) 63°, 31°
option b) 45°, 60°
option c) 28°, 87°
option d) 90°, 45°

Answer 1

The unknown angle measures for the four options are calculated by subtracting the sum of the given angles from 180°. They are found to be 86° for option (a), 75° for option (b), 65° for option (c), and 45° for option (d).

Step-by-step explanation:

To find the unknown angle measures in each triangle given the options (a) 63°, 31°; (b) 45°, 60°; (c) 28°, 87°; and (d) 90°, 45°, we use the fact that the sum of angles in a triangle is always 180°. For each option, we add the two provided angles and subtract their sum from 180° to find the unknown angle.

• For option (a): 63° + 31° = 94°, so the unknown angle is 180° - 94° = 86°.
• For option (b): 45° + 60° = 105°, so the unknown angle is 180° - 105° = 75°.
• For option (c): 28° + 87° = 115°, so the unknown angle is 180° - 115° = 65°.
• For option (d): 90° + 45° = 135°, so the unknown angle is 180° - 135° = 45°.

Thus, we have found the unknown angles for each option to be 86°, 75°, 65°, and 45° respectively.