Question

Which statements are true? Check all that apply.

The circumscribed angle L has a measure of 49°.
The circumscribed angle L has a measure of 65.5°.
If the measure of arc HJ is 98°, the measure of angle HMJ is 98°.
If the measure of arc HJ is 98°, the measure of angle HKJ is 98°.
If the measure of arc HJ is 98°, the measure of arc HK is 131°.

Answer 1

The circumscribed angle L has a measure of 49°.

If the measure of arc HJ is 98°, the measure of angle HMJ is 98°.

If the measure of arc HJ is 98°, the measure of arc HK is 131°.

Answer 2

True, 1, 3, 5

Explanation:

1. Angle L is sircumsribed angle, thenMJ⊥JL and MK⊥KL, so the measure of the angle L is

360°-131°-90°-90°=49° (the sum of all interior angles in the quadrilateral is 360°)

True

2. False, because m∠L=49°.

3. If the measure of arc HJ is 98°, then the measure of the central angle HMJ is 98°.

True

4. If the measure of arc HJ is 98°, then the measure of the central angle HMJ is 98° and the meausre of inscribed angle HKJ subtended on the arc HJ is half of the central angle measure and is equal to 49°.

False

5. If the measure of arc HJ is 98°, then the measure of the arc HK is

360°-131°-98°=131°

True