Question

Question 1(Multiple Choice Worth 2 points)

(09.03)

In circle A below, ∠BAE ≅ ∠DAC.



What is the mED?
82°
87°
98°
164°

Answer 1

Given ∠ BAE = ∠ DAC
=> the two angles are vertical angles
=> BAD and CAE are both straight lines.

Also given
12x-10 = ∠ BAE = ∠ DAC = 5x+53
=>
12x-10=5x-53
Solving for x gives
12x-5x=53+10
=> x=9
=> ∠ BAE = ∠ DAC = 9*12-10 = 98 °

Since BAD is a straight line,
∠ BAE and DAE are supplementary,
=>
BAE + DAE = 180 °
=> ∠ DAE=180-BAE=180-98=82 °
=>
Measure of arc ED = 82 °