Question

The three angles of a quadrilateral are in the ratio 2:3:5. The sum of the greatest and the smallest among these angles is 150°. What is the measure of the fourth angle?

Answer 1

Let the common ratio be x.

Then the three angles of a quadrilateral are 2x,3x,5x.

Given that sum of the greatest and the smallest among these angles is 150.

= > 5x + 2x = 150

= > 7x = 150

= > x = 150/7

= > x = 21.4.

Now,

Measure of angle A = 2(21.4)

= 42.8

Measure of angle B = 3(21.4)

= 64.2

Measure of angle C = 5(21.7)

107.

We know that sum of angles of a quadrilateral is 360.

= > 360 - (42.8 + 64.2 + 107)

= > 146.

Therefore, the measure of the fourth angle is 146.

Hope this helps!

Answer 2

Ratio of three angles of a quadrilateral=> 2:3:5
Let the three angles be 2x, 3x, and 5x
According to the question
5x +2x= 150°
7x = 150°
x = 150°/7=21.4° (Approximately)
Hence the three angles are
2x= 2×21.4°= 42.8°
3x = 3 × 21.4° = 64.2°
5x = 5×21.4° = 107°
Let the fourth angle be z
42.8°+64.2°+107°+z =360° (we know that sum of four angles of a quadrilateral is 360°)
214°+z =360°
z = 360°- 214°= 146°
Fourth angle = 146°