Question

Identify m∠BHJ.

The figure shows a circle with two tangents B H and J H. The secants intersect at point H in the exterior of the circle. The measure of arc B J is 105 degrees.

Answers:
m=52.5
m=127.5
m=70
m=75

Answer 1

m∠BHJ = 75°

Explanation:

It is given that mBJ=105∘

Find mBMJ

mBMJ=360∘−105∘=255∘

If two tangents intersect in the exterior of a circle, then the measure of the angle formed is half the difference of the measures of its intercepted arcs. So,

m∠BHJ=12(mBMJ−mBJ)

Substitute the given values and simplify.

m∠BHJ=12(255∘−105∘)

=12(150∘)

=75∘

Therefore, m∠BHJ=7

Answer 2

m∠BHJ = 75°

Explanation:

It is given that mBJ=105∘

Find mBMJ

mBMJ=360∘−105∘=255∘

If two tangents intersect in the exterior of a circle, then the measure of the angle formed is half the difference of the measures of its intercepted arcs. So,

m∠BHJ=12(mBMJ−mBJ)

Substitute the given values and simplify.

m∠BHJ=12(255∘−105∘)

=12(150∘)

=75∘

Therefore, m∠BHJ=75∘