**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°**