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Find the measures of angles 1 and 2. If necessary, round to the tenths place.

Hint: Do not assume that Point D is the center of the circle.


A. m<1 = 20 m<2= 20

B. m<1 =40 m<2 = 140

C. m<1 = 82.5 m<2 = 97.5

D. m<1 =97.5 m<2= 82.5

Find the measures of angles 1 and 2 If necessary round to the tenths place Hint Do not assume that Point D is the center

Answer :

Answer:

Option C

Step-by-step explanation:

From the picture attached,

m∠ABC = 40° [Given]

Since, measure of the intercepted arc is double of the measure of the inscribed angle.

Therefore, m(arc AC) = 2(m∠ABC)

m(arc AC) = 2(40°)

= 80°

m(arc FB) = 115° [Given]

By applying theorem of the angles formed by the chords inside a circle,

m∠2 = [tex]\frac{1}{2}(\text{arc}AC+\text{arc}FB)[/tex]

= [tex]\frac{1}{2}(80^{\circ}+115^{\circ})[/tex]

= 97.5°

m∠1 + m∠2 = 180° [Linear pair of angles are supplementary]

m∠1 + 97.5° = 180°

m∠1 = 180° - 97.5°

= 82.5°

Option C is the answer.

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