Answer:
mArc A B = 120° (C)
Step-by-step explanation:
Question:
In circle O, AC and BD are diameters.
Circle O is shown. Line segments B D and A C are diameters. A radius is drawn to cut angle D O C into 2 equal angle measures of x. Angles A O D and B O C also have angle measure x.
What is mArc A B?
a)72°
b) 108°
c) 120°
d) 144°
Solution:
Find attached the diagram of the question.
Let P be the radius drawn to cut angle D O C into 2 equal angle measures of x
From the diagram,
m Arc AOC = 180° (sum of angle in a semicircle)
∠AOD + ∠DOP + ∠COP = 180° (sum of angles on a straight line)
x° +x° + x° =180°
3x = 180
x = 180/3
x = 60°
m Arc DOB = 180° (sum of angle in a semicircle)
∠AOB + ∠AOD = 180° (sum of angles on a straight line)
∠AOB + x° = 180
∠AOB + 60° = 180°
∠AOB = 180°-60°
∠AOB = 120°
mArc A B = 120°
