If the exterior angle of a triangle is 120 degrees, what is the measure of the s

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Question: If the exterior angle of a triangle is 120 degrees, what is the measure of the smallest interior angle?

Options:

30 degrees
40 degrees
60 degrees
80 degrees

Correct Answer: 80 degrees

Solution:

The exterior angle is equal to the sum of the two opposite interior angles. If the exterior angle is 120 degrees, the smallest interior angle can be calculated as 180 - 120 = 60 degrees.

If the exterior angle of a triangle is 120 degrees, what is the measure of the s

Practice Questions

If the exterior angle of a triangle is 120 degrees, what is the measure of the smallest interior angle?

30 degrees
40 degrees
60 degrees
80 degrees

Questions & Step-by-Step Solutions

If the exterior angle of a triangle is 120 degrees, what is the measure of the smallest interior angle?

Step 1: Understand that an exterior angle of a triangle is formed when one side of the triangle is extended.
Step 2: Remember that the exterior angle is equal to the sum of the two opposite interior angles.
Step 3: In this case, the exterior angle is given as 120 degrees.
Step 4: To find the sum of the two opposite interior angles, we can use the formula: Sum of opposite interior angles = Exterior angle.
Step 5: Therefore, the sum of the two opposite interior angles is 120 degrees.
Step 6: The interior angles of a triangle always add up to 180 degrees.
Step 7: To find the smallest interior angle, we can subtract the sum of the two opposite angles from 180 degrees: 180 - 120 = 60 degrees.
Step 8: Thus, the smallest interior angle is 60 degrees.

Exterior and Interior Angles of a Triangle – The relationship between exterior angles and the sum of the opposite interior angles in a triangle.
Triangle Angle Sum Property – The sum of the interior angles of a triangle is always 180 degrees.

If the exterior angle of a triangle is 120 degrees, what is the measure of the s

What’s inside this PDF?

If the exterior angle of a triangle is 120 degrees, what is the measure of the s

Practice Questions

Questions & Step-by-Step Solutions

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