Answer:
The measure of angle M is [tex]\angle M=105[/tex]°.
Step-by-step explanation:
Given:
The triangles ΔMAP and ΔBOR are similar triangles.
[tex]\angle P=33[/tex]°, [tex]\angle O=42[/tex]°
If two triangles are similar, then their corresponding angles are also congruent.
ΔMAP is similar to ΔBOR,
[tex]\angle A\cong \angle O\\\because \angle O=42\\\therefore \angle A=42[/tex]
Now, for triangle ΔMAP, sum of all of its interior angles is 180 degrees.
Therefore,
[tex]\angle M+\angle A+\angle P=180\\\angle M+42+33=180\\\angle M+75=180\\\angle M=180-75\\\angle M=105[/tex]
Therefore, the measure of angle M is [tex]\angle M=105[/tex]°.
