Question

Use the diagram at the right for questions 1 – 4.

In △ABC, m∠ABC= 75 and m∠C = 40. If BP bisects ∠ABC and BQ is an altitude, find the measure of each angle.

1. ∠PBC

2. ∠CAB

3. ∠BQA

Answer 1

m∠PBC=37.5°, m∠CAB=65°, m∠BQA=90°

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°