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A triangle is shown.

What is the measure of angle x?

34
°
34°

56
°
56°

124
°
124°

146
°
146°

A triangle is shown. What is the measure of angle x? 34 ° 34° 56 ° 56° 124 ° 124° 146 ° 146°-example-1

1 Answer

3 votes

Explanation:

the sum of all angles in a triangle is always 180°.

the triangle here has 2 known angles : 56° and 90°.

so, the third angle must be

180 - 56 - 90 = 34°

x is now the supplementary angle to this third inner angle of the triangle.

that means together they have 180°.

simply because the sum of all angles around a single point on one side of a line is always 180° (as this simulates a half-circle with the center at this point).

so,

34 + x = 180

x = 180 - 34 = 146°

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