If the measure of AngleB is 40°, what measures can AngleA and AngleC be? Select the three correct answers.

Question

20° and 30°
30° and 110°
55° and 85°
60° and 90°
70° and 70°

Answer 1

The sum of the interior angles in a triangle is always 180°.

If Angle B is 40°, we can determine the possible measures for Angle A and Angle C by using the equation:

Angle A + Angle B + Angle C = 180°

Substituting the value of Angle B:

Angle A + 40° + Angle C = 180° Angle A + Angle C = 180° - 40° Angle A + Angle C = 140°

Now we can evaluate the proposed pairs:

1. 20° and 30°:

   • 20° + 30° = 50° (not valid)

2. 30° and 110°:

   • 30° + 110° = 140° (valid)

3. 55° and 85°:

   • 55° + 85° = 140° (valid)

4. 60° and 90°:

   • 60° + 90° = 150° (not valid)

5. 70° and 70°:

   • 70° + 70° = 140° (valid)

The three correct measures for Angle A and Angle C are:

• 30° and 110°
• 55° and 85°
• 70° and 70°