Question

A parallelogram has one angle that measures 140°. What are the measures of the other three angles in the parallelogram?

Answer 1

Answer:

let angle A=140°

then ,

angle A=angle C=140°(opposite angle of parallelogram )

angle A+angle B=180°

angle B=(180-140)°

angle B=angle D=40°

Answer 2

Final Answer:

The measures of the other three angles in the parallelogram are 40 degrees, 140 degrees and 40 degrees respectively.

Given:

A parallelogram has one angle that measures 140 degrees.

To Find:

The measures of the other three angles in the parallelogram.

Explanation:

The following points are relevant for solving this problem.

• The sum of the interior angles of a parallelogram is equal to three hundred and sixty degrees.
• The opposite angles of a parallelogram are equal to each other.

Step 1 of 3

Abiding by the statement that the parallelogram has one angle that measures 140 degrees, the value of its opposite angle.

$=140\textdegree$

Step 2 of 3

In line with the property of a parallelogram, the sum of the other two angles of the parallelogram is

$=360-2\times 140\\=360-280\\=80\textdegree$

Step 3 of 3

Again, from the fact that the opposite angles of a parallelogram are equal to each other, each of the rest other two angles of the parallelogram is

$=\frac{80}{2} \\=40\textdegree$

Therefore, when one angle measures 140 degrees in a parallelogram the required measures of the other three angles in the parallelogram are 40 degrees, 140 degrees and 40 degrees respectively.

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