Question

In the given diagram, what is the measure of ∠ABC of parallelogram ABCD?

Answer 1

Answer: C) 136 degrees

The known acute angle of the triangle is 46 degrees, so the unknown acute angle of that triangle is 90-46 = 44 degrees. In other words, the two acute angles of any right triangle must add to 90, so 46+44 = 90.

The 44 degree angle is adjacent to angle ADC, and it adds to angle ADC to form 180 degrees.

If x is the measure of angle ADC, then

44+(angleADC) = 180

44+x = 180

x = 180-44

x = 136

angle ADC = 136 degrees

For any parallelogram, the opposite angles are always congruent. Therefore, angle ABC is equal to angle ADC = 136, making ABC = 136 as well.

Answer 2

Answer: C. 136 degrees

Explanation:

From the diagram, angle C is a right angle because it is formed by a perpendicular line. It means that

Angle BCD + 46 = 90

angle BCD = 90 - 45 = 44 degrees

The opposite angles in a parallelogram are equal while the adjacent angles are supplementary. Angle ABC and angle BCD are supplementary and the sum of supplementary angles is 180 degrees. Therefore,

Angle ABC + 44 = 180

Angle ABC = 180 - 44

Angle ABC = 136 degrees