Question

In parallelogram abcd ∠a=152°. what is the measure of ∠d?

Answer 1

Please read the explanation.

Explanation:

A Parallelogram has many important properties:

A parallelogram is a four-sided polygon.

Analyze the image of a parallelogram:

Hence, in the picture above,

`AB | | DC`

`AD | | BC`

In a parallelogram, opposite sides and opposite angles are congruent.

Hence,

`AB ~= DC`

`AD ~= BC`

and

`/_ BAD ~= /_BCD`

`/_ ABC ~= /_ADC`

An important property of a parallelogram:

Consecutive Interior Angles are Supplementary.

Hence,

It is given that

`/_ BAD = 152^@`

As Consecutive interior angles are supplementary in a parallelogram,

`/_ BAD + /_ ADC = 180^@`

`/_ ADC = 180^@ - /_ BAD`

`/_ ADC = 180^@ - 152^@`

`/_ ADC = 28^@`

Hence, the required result is `color(blue)(/_D = 28^@`

Please refer to the resultant parallelogram image below:

Hope the solution is helpful.