Question

if hj is the angle - bisector of ∠ahb, select all of the answers below that describe a true statement. m∠ahb = 90, m∠1 + m∠2 = m∠ahb, m∠bha = 2(m∠2)

Explanation:

Step1: Recall angle - bisector property

If HJ is the angle - bisector of ∠AHB, then ∠1 = ∠2 and ∠AHB=∠1 + ∠2.

Step2: Analyze each statement

Statement 1: m∠AHB = 90

There is no information given to suggest that ∠AHB is a right - angle. So, we cannot say this is true.

Statement 2: m∠1 + m∠2 = m∠AHB

By the angle - addition postulate, the measure of the whole angle (∠AHB) is equal to the sum of the measures of its non - overlapping parts (∠1 and ∠2). So, this statement is true.

Statement 3: m∠BHA = 2(m∠2)

Since ∠1 = ∠2 and ∠BHA=∠1 + ∠2, then ∠BHA = 2(m∠2). This statement is true.

Answer:

m∠1 + m∠2 = m∠AHB, m∠BHA = 2(m∠2)