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Question 1(Multiple Choice Worth 2 points)

(09.03)

In circle A below, ∠BAE ≅ ∠DAC.



What is the mED?
82°
87°
98°
164°

Question 1Multiple Choice Worth 2 points 0903 In circle A below BAE DAC What is the mED 82 87 98 164 class=

Respuesta :

mathmate
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 °

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