The measures of the four interior angles of a quadrilateral are $x, 2x, x 20,$ and $x 40$ degrees. How many degrees are in the measure of the largest interior angle of the quadrilateral?

Question

Mathematics

Gia

1 May, 05:37

The measures of the four interior angles of a quadrilateral are $x, 2x, x 20,$ and $x 40$ degrees. How many degrees are in the measure of the largest interior angle of the quadrilateral?

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Answers (1)

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Quinten Hebert · Answer 1

The largest interior angle is 100 degrees

Step-by-step explanation:

If the measures of the four interior angles of a quadrilateral are x, 2x, x+20 and x+40

Total Interior Angle of a Quadrilateral = 360 degrees

Therefore: x+2x+x+20+x+40=360

6x+60=360

6x=360-60

6x=300

Divide both sides by 6

x=50

Since x=50, Therefore the angles of the quadrilateral are

x=50,

2x = (2X50),=100

x+20 = (50+20) = 70

and x+40 = (50+40) = 90

The largest interior angle is 100 degrees