Question

in the diagram below, ad || eh, m∠abf = 138° and m∠cgh = 82°. find m∠i.
you may assume lines that appear straight are straight, but the figure is not otherwise drawn to scale.
answer attempt 1 out of 2
m∠i =
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Explanation:

Step1: Find the measure of the angle adjacent to ∠ABF

Since ∠ABF = 138°, the adjacent - angle to ∠ABF (let's call it ∠FBC) is 180°−138° = 42° because they are linear - pair angles and the sum of linear - pair angles is 180°.
180 - 138=42

Step2: Use the property of parallel lines

Because AD∥EH, ∠FBC and the angle corresponding to it with respect to the parallel lines AD and EH (let's call it ∠BGE) are equal. So ∠BGE = 42°.
∠BGE = ∠FBC = 42°

Step3: Find the measure of ∠I

In the triangle formed by points G, F, and I, we know that ∠CGH = 82°, and ∠CGH and ∠BGF are vertical angles, so ∠BGF=82°.
The sum of the interior angles of a triangle is 180°. In triangle GFI, if we let ∠I = x, then x + 42°+82° = 180°.
x=180-(42 + 82)
x = 56°

Answer:

56