Question

Given triangle ABC is congruent to DEC find m

Answer 1

First, we know that angle B is congruent to angle E.

2x + 40 = 5x + 10

2x + 30 = 5x

30 = 3x

x = 10

Angle B and Angle E = 60 degrees

Angle C = 14 degrees

Remember that the interior angles of a triangle always add up to 180 degrees. Now that we know 2 of the 3 angles of these triangles, and because they are congruent, all that's left to do is find Angle A/D by setting up a simple equation.

60 + 14 + D = 180

74 + D = 180

D = 106

Angle D = 106 degrees

Hope this helps!

Answer 2

Explanation:

<E = <A property of congruency.

<A = 5x + 10 Comes from the fact that <A and <E are equal.

Three angles of the triangle are given. They add to 180 degrees.

2x + 40 + x + 4 + 5x + 10 = 180 Combine like terms

8x + 54 = 180 Subtract 54 from both sides.

8x + 54 - 54 = 180 - 54 Combine

8x = 126 Divide by 8

8x/8 = 126/8

x = 15.75

<B = <D Congruency and parallel lines

<D = 2x + 40 Substitute for x

<D = 2*15.75 + 40 Combine

<D = 31.5 + 40

<D = 71.5