Question

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

Answer 1

Option C

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 =
`(1)/(2)(\text{arc}AC+\text{arc}FB)`

=
`(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.