Question

In the given figure, if the angles a and b are in the ratio 2 : 3, then angle c is:

a) 90°

b)126°

c) 144°

d) Obtuse angle​

Answer 1

Answer:

Step-by-step explanation:

given that , ∠a : ∠b = 2 : 3 .

let the angles be 2x and 3x .

as from the figure we can see that ∠a + ∠b = 90° . {right angle}

so ,

2x + 3x = 90

5x = 90

x = 90 / 5

x = 18

∠a = 2x = 18 × 2 = 36°

∠b = 3x = 3 × 18 = 54°

from figure we can see that ∠a and ∠c are on a straight line .

so , ∠a + ∠c = 180° {linear angles}

36 +∠c = 180

∠c = 180 - 36

∠c = 144°

hence , ∠c is 144° .

Answer 2

Given - Angles a and b are in ratio 2:3

Find - Measure of angle c

Solution - Let us say that angle a and angle are 2x and 3x.

As evident from the figure, combined angle a and angle b are equal to 90°.

So, 2x + 3x = 90°

5x = 90°

x = 18°

Angle a = 2x

Angle a = 2*18

Angle a = 36°

Angle b = 3x

Angle b = 3*18

Angle b = 54°

Further, as per the figure combined angle a and angle c is equal to 180°.

So, 36° + angle c = 180°

Angle c = 144°.

Therefore, c) 144° is the correct answer about angle c in given figure.