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°.

Explanation:

Step1: Find arc HJ

Arc $HJ = \angle HMJ = 131^\circ$

Step2: Find arc HKJ

Arc $HKJ = 360^\circ - 131^\circ = 229^\circ$

Step3: Calculate circumscribed angle L

Circumscribed angle formula: $\frac{1}{2}(\text{larger arc} - \text{smaller arc})$
$\angle L = \frac{1}{2}(229^\circ - 131^\circ) = 49^\circ$

Step4: Check arc HJ=98° statements

• Central angle $\angle HMJ$ equals arc $HJ$, so $\angle HMJ=98^\circ$.
• Inscribed angle $\angle HKJ = \frac{1}{2}\times\text{arc }HJ = 49^\circ

eq 98^\circ$.

• Arc $HK = \frac{1}{2}(360^\circ - 98^\circ) = 131^\circ$.

Answer:

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°.