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Consider the following diagram. Figures ABED and EFJH represent congruent trapezoids, and figures BCFE and DEHG represent congruent parallelograms. Points A, B, and C are collinear, as are points D, E, and F. If m<1 = (3x - 5) and m<2 = (2x + 15), then what is the measure of <3?

Consider the following diagram Figures ABED and EFJH represent congruent trapezoids and figures BCFE and DEHG represent congruent parallelograms Points A B and class=

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The measure of m∠3 =20°

Step-by-step explanation:

Given that:

m∠1 = (3x-5)° and m∠2= (2x+15)° then

∠ABE= m∠1= opposite vertical angles are equal

∠ABE =∠BEF = alternate angles

m∠2= ∠BEF = opposite vertical angles are equal

Thus m∠1 = m∠2

(3x-5)° = (2x+15)°

3x-5=2x+15

3x-2x=15+5

x=20°

m∠2 and m∠3 are opposite angles in the parallelogram DEHG which are congruent thus m∠3 =20°

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Angles in a parallelogram:https://brainly.com/question/11611069

Keywords : congruent, trapezoids, parallelogram, collinear, points

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