So the question says...

Suppose you have ∠SMB and m ∠SMB =125.35 °.

Part A: Determine the angle measure that is complement to ∠SMB, if possible. If ∠SMB does not have a complementary angle, then explain why it does not.

Part B: Determine the angle measure of the supplement of ∠SMB.

Part C: Determine the angle measure of the angle complement to ∠SMB’s supplement.

I’m stuck on this question so if anyone can help me with it that would be greatly appreciated. Thanks!

Part A. Two angles are complementary if their sum is equal to 90°. Since the angle given is more than 90°, there is no possible complement for a 125.35-degree angle.

Part B. Two angles are supplementary if their sum is equal to 180°. So,
Supplementary angle = 180 - 125.35 = 54.65°

Part C. Complementary angle = 90 - 54.65 = 35.35°

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Abdulazeez10 Abdulazeez10 · Answer 2 · 2021-10-04T13:30:18+02:00

Part A: ∠SMB does not have a complementary angle

Part B: The angle measure of the supplement of ∠SMB is 54.65°

Part C: The angle measure of the angle complement to ∠SMB's supplement is 35.35°

The given angle is ∠SMB and m ∠SMB =125.35 °

For Part A

Complementary angles are angles that sum up to 90°.

To determine the angle measure that is complement to ∠SMB, we will find the angles that adds up to ∠SMB to give 90°. Since ∠SMB is already greater than 90°, therefore, ∠SMB does not have a complementary angle.

For Part B.

Supplementary angles are angles that sum up to 180°.

To determine the angle measure of the supplement of ∠SMB, we will find the angle that adds up to ∠SMB to give 180°. Let the measure of the angle be x, that is

x + 125.35° = 180°

∴ x = 180° - 125.35°

x = 54.65°

∴ The angle measure of the supplement of ∠SMB is 54.65°

For Part C

To determine the angle measure of the angle complement to ∠SMB's supplement, we will determine the measure of the angle that adds up to ∠SMB's supplement to give 90°. Let the angle be y

Then,

y + 54.65° = 90°

(NOTE: ∠SMB's supplement is 54.65°)

∴ y = 90° - 54.65°

y = 35.35°

∴ The angle measure of the angle complement to ∠SMB's supplement is 35.35°

Hence,

Part A: ∠SMB does not have a complementary angle

Part B: The angle measure of the supplement of ∠SMB is 54.65°

Part C: The angle measure of the angle complement to ∠SMB's supplement is 35.35°

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