Question

Use the diagram to find the measurement of each of the angles

Answer 1

Answer:

1. ∠LOQ = 80°

2. ∠LRQ = 40°

3. ∠LBQ = 40°

Step-by-step explanation:

• The measure of a central angle (angle that goes to the center of the circle) is EQUAL to the ARC from which it is intercepted.
• The measure of the angle that is on opposite side, on the circumference, of the circle is HALF of the ARC from which it is intercepted.

It is given that ARC QL has a measure of 80.

• Central angle from ARC QL (with same measure) are angle LOQ only.
• Opposite angles (half of measure of ARC QL) from ARC QL (on opposite side on circumference) are angles LRQ and LBQ.

1.

m∠LOQ: ∠LOQ is the central angle from ARC QL so it has SAME MEASURE.

∠LOQ = 80°

2.

m∠LRQ: ∠LRQ is the opposite angle from ARC QL so it is HALF of ARC QL.

∠LRQ = $\frac{1}{2}(80)=40$

∠LRQ = 40°

3.

m∠LBQ: ∠LBQ is also another opposite angle from ARC QL so it is HALF of ARC QL as well.

∠LBQ = $\frac{1}{2}(80)=40$

∠LBQ = 40°