In a quadrilateral ABCD, if angle A is 70 degrees and angle B is 110 degrees, wh

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Question: In a quadrilateral ABCD, if angle A is 70 degrees and angle B is 110 degrees, what can be inferred about angles C and D?

Options:

Correct Answer: They must be supplementary.

Solution:

The sum of the angles in a quadrilateral is 360 degrees. Therefore, angles C and D must sum to 180 degrees, making them supplementary.

In a quadrilateral ABCD, if angle A is 70 degrees and angle B is 110 degrees, what can be inferred about angles C and D?

In a quadrilateral ABCD, if angle A is 70 degrees and angle B is 110 degrees, what can be inferred about angles C and D?

Step 1: Understand that a quadrilateral has four angles: A, B, C, and D.
Step 2: Know that the total sum of all angles in a quadrilateral is always 360 degrees.
Step 3: Identify the given angles: angle A is 70 degrees and angle B is 110 degrees.
Step 4: Add the measures of angles A and B together: 70 degrees + 110 degrees = 180 degrees.
Step 5: Subtract the sum of angles A and B from 360 degrees to find the sum of angles C and D: 360 degrees - 180 degrees = 180 degrees.
Step 6: Conclude that angles C and D must sum to 180 degrees, which means they are supplementary.

Sum of Angles in a Quadrilateral – The total measure of the interior angles in any quadrilateral is always 360 degrees.
Supplementary Angles – Two angles are supplementary if their measures add up to 180 degrees.