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Answer:
m∠<em>DEB</em> = _<u>70</u>_°
m∠<em>BCD</em>= _<u>110</u>_°
m∠<em>EAB</em>= _<u>73</u>_°
Step-by-step explanation:
<u>To find ∠</u><em><u>DEB</u></em><u>: </u>
Take the angle of ∠<em>EDC</em>, which is 110°. We know the total degree in a triangle is 180°. So, we do 180° - 110° to get 70°.
<u>To find ∠</u><em><u>BCD</u></em><u>: </u>
Because <em>EBCD</em> is an isosceles trapezoid, this means that ∠<em>D</em> and ∠<em>C</em> both have the congruent angles. Since we know ∠<em>EDC</em> is 110°, this means that ∠<em>C</em> is also 110°.
<u>To find ∠EAB: </u>
We know that m∠<em>ABC</em> is 133° and ∠<em>DEA</em> is 114°. However, both angles count both the triangle and trapezoid. Previously we figured out that ∠<em>DEB</em> is 70°. We'll take the angle of ∠<em>DEA</em> and subtract the angle of ∠<em>DEB</em> from it, which gets us 44°. To figure out the angle of ∠<em>B</em>, we take the angle of ∠<em>ABC</em> and subtract 70° or the angle of ∠<em>DEB</em>, which gets us 63°. Now we take the total degree of a triangle, 180° and minus both 44° and 63° from it, which is 73°.
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