Question

MAP-ABOR. In MAP
P=33 and in BOR 30
42. Find the measure of M​

Answer 1

The measure of angle M is
`\angle M=105`°.

Explanation:

Given:

The triangles ΔMAP and ΔBOR are similar triangles.

`\angle P=33`°,
`\angle O=42`°

If two triangles are similar, then their corresponding angles are also congruent.

ΔMAP is similar to ΔBOR,

`\angle A\cong \angle O\\\because \angle O=42\\\therefore \angle A=42`

Now, for triangle ΔMAP, sum of all of its interior angles is 180 degrees.

Therefore,

`\angle M+\angle A+\angle P=180\\\angle M+42+33=180\\\angle M+75=180\\\angle M=180-75\\\angle M=105`

Therefore, the measure of angle M is
`\angle M=105`°.