Question

(a) In the figure below, m AB = 106° and m CD =66. Find mAEB

Answer 1

`\huge\boxed{\sf \angle AEB=86 \textdegree}`

Explanation:

Given:

arc AB = 106°

arc CD = 66°

Statement:

• According to angles of intersecting chords theorem, the measure of angle formed by two intersecting chords is half the sum of arcs intercepted by the angle.

Mathematical form:

`\displaystyle \angle AEB=(1)/(2) (arc \ AB+arc \ CD)`

Solution:

Put the given data in the above formula.

`\displaystyle \angle AEB=(1)/(2) (106 + 66)\\\\\angle AEB=(1)/(2) (172)\\\\\angle AEB=86 \textdegree \\\\\rule[225]{225}{2}`