Question

The measures of the angles of a quadrilateral are in the ratio 2:4:5: 7. Find th
measure of each of its angles.​

Answer 1

Given

The measure of the angles of a quadrilateral are in the ratio 2:4:5:7 .

To Find

Measure of each angle

$\sf\huge\bold{\underline{\underline{{Solution}}}}$

Let the first angle be 2x

second angle be 4x

third angle be 5x

and the fourth angle be 7x

according to the question:

We know that the sum of all Interior angles of a quadrilateral is 360°.

=>1st angle + 2nd angle +3rd angle + fourth angle =360°

=>2x+4x+5x+7x=360°

=>18x=360°

=>x= 360/18

=>x=20°

Finding all angles :

first angle = 2x=2×20°=40°

second angle = 4x=4×20°=80°

third angle = 5x=5×20°=100°

fourth angle = 7x=7×20°=140°

Check:

Sum of measures of all angles must be equal to 360°

=>40°+80°+100°+140°

=>220°+140°=360°

Alternative Method

First angle = 2/18×360 = 40°

second angle = 4/18×360°=4×20°=80°

Third angle = 5/18×360°=5×20°=100°

Fourth angle = 7/18×360°=7×20°=140°

Answer 2

Let all angles is 2x, 4x, 5x, 7x

sum of all angles =360°

2x+4x+5x+7x=360°

18x=360°

x=360/18

x=20°

2x= 20×2= 40°

4x= 20×4=80°

5x= 20×5= 100°

7x= 20×7= 140°

All angles are 40°, 80°, 100°, 140°

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