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How many degrees is angle x?

A normal-level "Angle" problem."Equal sides mean equal angles." That one sentence solves every isosceles-triangle problem.

GivenAB and AC have the same length (isosceles triangle)

Angle ★★★☆☆☆ How many degrees is angle x? 40° x ABC

Hints

  1. Sides AB and AC are the same length (see the marks). In a triangle with two equal sides, the two base angles are equal too. So bottom-left and bottom-right are the same size.
  2. Cut off the three angles and gather them at one point below.
  3. Laid out they make a straight line, i.e. 180°. It consists of "one apex angle" and "two equal x's".
  4. Removing the 40° apex from 180° leaves 140°. That is two x's.
  5. Two x's make 140°, so 140 ÷ 2 is the answer.

Answer 70°

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