10
QuizMultiple Select

Sum of Interior Angles of a Triangle

Question 10 • *Integrated Math II Full

The measure of one angle of a triangle is 105°. What do you know about the measures of the other two angles? Check all that apply.

Answer
A
Both angles are acute.
B
The sum of the measures of the two angles is 75°.
C
The sum of the measures of the two angles is 155°.
D
One of the angles is a right angle.
E
The measure of neither angle is more than 75°.
F
The measures of the other angles must be 105° too.
G
The measure of one of the other angles equals 75°.
H
The measure of one of the other angles must be 45°.

Explanation

The angles in a triangle add up to 180°, so the other two angles sum to 180° − 105° = 75°. Both must be less than 75° because each is positive and together they total 75°; therefore, both are acute and neither is more than 75°. The other angles do not have to be equal, so one is not necessarily 75° or 45°.

AI-written and checked against the verified answer.