In \triangle ABC, the measure of exterior angle \angle BCD is 115^\circ. If the measure of… — ACT

In $\triangle ABC$ , the measure of exterior angle $\angle BCD$ is $115^\circ$ . If the measure of interior angle $\angle A$ is $45^\circ$ , what is the measure, in degrees, of interior angle $\angle B$ ?

Answer: 70 degrees

Answer

The measure of interior angle

\angle B

70

degrees.

By the Exterior Angle Theorem, the measure of exterior angle

\angle BCD

is equal to the sum of the two remote interior angles,

\angle A

and

\angle B

. We can write this relationship as

m\angle BCD = m\angle A + m\angle B

. Substituting

115^\circ

for

m\angle BCD

and

45^\circ

for

m\angle A

gives

115 = 45 + m\angle B

. Solving for

m\angle B

yields

70^\circ

Step-by-Step Solution

Set up the equation using the Exterior Angle Theorem.

m\angle BCD = m\angle A + m\angle B

The measure of an exterior angle of a triangle is equal to the sum of the measures of its two remote interior angles.

Substitute the given measurements into the equation.

115 = 45 + m\angle B

The exterior angle

\angle BCD

measures

115^\circ

and the remote interior angle

\angle A

measures

45^\circ

Solve for the unknown angle measure by subtraction.

m\angle B = 70

Subtracting

45

from both sides isolates

m\angle B

Key Concept

Exterior Angle Theorem

Question

Answer

Step-by-Step Solution

Key Concept

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