Question

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.
Both angles are acute.
The sum of the measures of the two angles is 75°.
The sum of the measures of the two angles is 155°.
One of the angles is a right angle.
The measure of neither angle is more than 75°.
The measures of the other angles must be 105° too.
The measure of one of the other angles equals 75°.
The measure of one of the other angles must be 45°.

Answer 1

True:
- Both angles are acute. (Their measures must be positive and sum to 75°, so each is <90°.)
- The sum of the measures of the two angles is 75°. (180° − 105° = 75°.)
- The measure of neither angle is more than 75°. (If one were >75° the other would be negative; in fact each <75°.)

False:
- The sum is 155° (wrong).
- One is a right angle (90° impossible since the other would be negative).
- Both must be 105° (impossible, would sum >180°).
- One equals 75° (then the other would be 0°, not allowed).
- One must be 45° (not required).