Construct a quadrilateral ABCD so that the degree measure of angle A is 80 °, the degree measure of angle B

| July 3, 2021 | education

Construct a quadrilateral ABCD so that the degree measure of angle A is 80 °, the degree measure of angle B is 62.5% greater than the degree measure of angle A, And the degree measure of angle C is 20% greater than the degree measure of angle A. a) what is the degree measure of angle D? b) what is the sum of the angles of the quadrilateral? c) what percentage of the sum of the angles of the quadrilateral is the angle D?

Before construction, we define all the corners of the quadrilateral.

Determine the degree measure of the angle B, for which we compose the proportion and solve it.

80 – 100%

X0 – 62.5%.

80 / X = 100 / 62.5.

X = 80 * 62.5 / 100 = 50.

Angle B = 80 + 50 = 130.

Determine the degree measure of the angle C, for which we compose the proportion and solve it.

800 – 100%

X0 – 20%.

80 / X = 100/20.

X = 80 * 20/100 = 16.

Angle C = 16 + 80 = 96.

The sum of the angles of a convex quadrilateral is 360.

Determine the value of the angle D.

A + B + C = 80 + 130 + 96 = 306.

Angle D = 360 – 306 = 54.

Answer: 54.

Let’s determine what percentage 54 is from 360.

54 – X%.

360 – 100%.

X = 54 * 100/360 = 15%.

Answer: 15%.



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