# Angle ABE = 112 degrees Angle DCF = 68 degrees AC-9 cm Find side AB of triangle ABC.

October 5, 2021 | education

| The solution of the problem:

The corners FAE and FAC are adjacent corners. The sum of adjacent angles is 180 degrees.

Therefore, FAE + FAC = 180 degrees.

Let’s substitute the values we know:

112 degrees + FAC angle = 180 degrees.

FAC angle = 180 – 112 = 68 degrees.

Angles DBF and ABC are vertical. The vertical angles are equal.

Therefore, the angle DBF = ABC = 68 degrees.

Consider a triangle ABC:

Angle B and Angle A are 68 degrees.

It turns out that triangle ABC is isosceles.

So side AC = side BC = 9

Problem answer: side AB is 9.

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