Question

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

Answer 1

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 = $\frac{1}{2}(\text{arc}AC+\text{arc}FB)$

        = $\frac{1}{2}(80^{\circ}+115^{\circ})$

        = 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.