Question

What are the measures of Angles a, b, and c? Show your work and explain your answers.

30⁰
75°

Please help me

Answer 1

`\angle A=30^\circ\\\angle B=60^\circ\\\angle C=105^\circ`

Explanation:

Since
`\angle C` and
`75^\circ` are supplementary angles, they add up to
`180^\circ`. So,
`\angle C=180^\circ-75^\circ=105^\circ`.

Also, since
`\angle A` and
`30^\circ` are vertical angles, they have the same angle measure as the angles are congruent to each other. So,
`\angle A=30^\circ`.

We can easily figure out
`\angle B` because we have the measurement of
`\angle A` and a given right angle, which measures
`90^\circ`. Thus, by the Triangle Angle-Sum Theorem, all the interior angles of that triangle must add up to
`180^\circ`, so
`\angle A+\angle B+90^\circ=180^\circ` must hold true. Hence,
`30^\circ+\angle B+90^\circ=180^\circ\rightarrow \angle B=60^\circ`.