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I really dont know how to do this please help!

I really dont know how to do this please help!-example-1

1 Answer

4 votes

Angles ECD and ACB are congruent, since they form a pair of vertical angles. Let their measure by
y.

The sum of the interior angles of any triangle is 180°. This means

• in ∆CDE, we have


x + 100^\circ + y = 180^\circ

• in ∆ABC, we have


4x + 49^\circ + y = 180^\circ

Solve for
x by eliminating
y.


(x + 100^\circ + y) - (4x + 49^\circ + y) = 180^\circ - 180^\circ


-3x + 51^\circ = 0


3x = 51^\circ


\boxed{x = 17^\circ}

User Padilo
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