Question

Find mAB

B
E
C
A
23
11%
D
Segment and angle lengths are not drawn to scale.
Enter your answer in the box.

Answer 1

arc AB = 68°

Explanation:

You want the measure of arc AB whose parts are arc AE and EB with inscribed angles ADE = 11° and EDB = 23°.

Angle Addition

The measure of angle ADB is the sum of the measures of its parts:

∠ADB = ∠ADE +∠EDB

∠ADB = 11° +23° = 34°

Inscribed angle

The measure of an inscribed angle is half the measure of the arc it subtends. This means the arc measure is twice the inscribed angle measure.

arc AB = 2 × ∠ADB = 2 × 34°

arc AB = 68°