A right triangle has one angle that measures 77°. What is the measurement for the missing angle?

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Answer 1 · 2018-05-16T18:24:17

The missing angle is $13^{\circ}$ $13^@$

Let $∠ B$ $angleB$ be the missing angle.

Let $∠ A$ $angleA$ be the angle that measures $77^{\circ}$ $77^@$

Let $∠ C$ $angle C$ the right angle that measures $90^{\circ}$ $90^@$

The following is true of all triangles:

$∠ A + ∠ B + ∠ C = 180^{\circ}$ $angleA+angleB+angleC = 180^@$

Express the above equation as $∠ B$ $angleB$ in terms of the other angles:

$∠ B = 180^{\circ} - ∠ A - ∠ C$ $angleB = 180^@-angleA-angleC$

Substitute the values for $∠ A$ $angle A$ and $∠ C$ $angleC$

$∠ B = 180^{\circ} - 77^{\circ} - 90^{\circ}$ $angleB = 180^@-77^@-90^@$

$∠ B = 13^{\circ}$ $angleB = 13^@$