1 Answer

Padilo · Answer 1 · 2023-01-24T10:13:56+0000

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

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
by eliminating
.

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

$-3x + 51^\circ = 0$

$3x = 51^\circ$

$\boxed{x = 17^\circ}$

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