Answer:
m∠PBC=37.5°, m∠CAB=65°, m∠BQA=90°
Step-by-step explanation:
Given In △ABC, m∠ABC= 75° and m∠C = 40°. If BP bisects ∠ABC and BQ is an altitude.
Then we have to find the following measures.
Given BP bisects ∠ABC and m∠ABC= 75°
m∠ABC=m∠PBC+m∠PBA=75°
Hence, m∠PBC=m∠PBA=37.5°
In ΔABC, by angle sum property of triangle
m∠CAB+m∠ACB+m∠ABC=180°
⇒ m∠CAB+40°+75°=180°
⇒ m∠CAB=65°
As we know, altitude meets the base at right angles.
Now, given BQ altitude on the base AC.
Hence, m∠BQA=90°
