Question

Work out the value of angle x

Answer 1

Answer: 166 degrees

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Explanation:

The given exterior angle 97 is adjacent to the interior angle 180-97 = 83. This is the base angle of the isosceles triangle. The other base angle is directly above it. The base angles are always opposite the congruent sides.

The missing interior angle (adjacent to the blue angle x) is unknown, so we'll call it angle y. This angle adds to the other two base angles (83 each) to get a sum of 180. Adding any three interior angles of a triangle always gets you 180

y+83+83 = 180

y+166 = 180

y = 180-166

y = 14

Angle x and y are supplementary. They form a 180 degree angle

x+y = 180

x = 180-y

x = 180-14

x = 166

As you can see, the base angles combine to form the exterior angle we're after. This is because of the remote interior angle theorem.