Find D

Geometry Level 1

A = 2x

B = 0.5x

C = 2x

Find D.

3.5x 3x 90° 2x 100° 112.5°

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2 solutions

A + B + C = 180°

2x + 0.5x + 2x = 180°

2x + 0.5x + 2x = 4.5x

D = (A + B + C) - C

D = 4.5x - 2x = 2.5x

180°/4.5 = 40° = x

40° x 2.5 = D = 100°.

The sum of the interior angles of a triangle is 18 0 180^\circ . So we have

2 x + 2 x + 0.5 x = 180 2x+2x+0.5x=180 \implies 4.5 x = 180 4.5x=180 \implies x = 40 x=40

The angles are

A = 2 x = 2 ( 40 ) = 8 0 A=2x=2(40)=80^\circ

B = 0.5 x = 0.5 ( 40 ) = 2 0 B=0.5x=0.5(40)=20^\circ

C = 2 x = 8 0 C=2x=80^\circ

So D D is 360 80 80 2 = \dfrac{360-80-80}{2}= 10 0 \color{#D61F06}\boxed{100^\circ}

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