Question

Find the measures of the indicated angles in circle O. Which statement is NOT true? (The figure is not drawn to scale.)

Answer 1

ANSWER

a=53°

b=106°

c=74°

d=37°

EXPLANATION

A semicircle creates a right angle on the circumference.

d+53°=90°

d=90°-53°

d=37°

Angle subtended at the center by an arc is twice the angle subtended at the circumference by the same arc.

c=2d

c=2(37)

c=74°

Adjacent angles on a straight line add up to 180°

c+b=180°

b=180°-c

b=180°-74°

b=106°

The sum of interior angles in an isosceles triangle is 180°

a+a+c=180°

2a+74=180

2a=180-74

2a=106

a=53°