Question

How does one go about completing this?

Answer 1

• 100°

Explanation:

∠AEC ≅ ∠BED as vertically opposite angles

• m∠AEC = m∠BED = 1/2(mAC + mBD), angles between intersecting chords

Substitute values and solve for x:

• 4x = 1/2(120 + 2x)
• 4x = 60 + x
• 3x = 60
• x = 20

Find the measure of AEC:

• m∠AEC = 4*20 = 80°

AED and AEC form a linear pair hence supplementary:

• m∠AED = 180° - m∠AEC

Find the measure of ∠AED:

• m∠AED = 180° - 80° = 100°