Question

(6) One of the angles of a triangle is equal to the sum of the other two angles. If the ratio of the other two angles is 4 : 5, then the angles of triangle are
a. 40°,509,90°
b. 409,60°,80°
c. 500,50°,80°
d. 50°,609,70°​

Answer 1

Answer:-

Given:

Sum of two angles of a triangle is equal to the measure of third angle.

Ratio of first two angles = 4 : 5

Let the measures of two angles be 4x , 5x.

Hence,

Third angle = 4x + 5x = 9x.

We know that,

Sum of three angles of a triangle = 180°

⟶ 4x + 5x + 9x = 180

⟶ 18x = 180

⟶ x = 180/18

⟶ x = 10

Hence,

• 1st angle = 4x = 4(10) = 40°

• 2nd angle = 5x = 5(10) = 50°

• 3rd angle = 9x = 9(10) = 90°

Therefore, the three angles of the given triangle are 40° , 50° , 90° (Option - a).

Answer 2

Correct Question :-

One of the angles of a triangle is equal to the sum of the other two angles. If the ratio of the other two angles is 4 : 5, then the angles of triangle are :-

a. 40°,50°,90°

b. 40°,60°,80°

c. 50°,50°,80°

d. 50°,60°,70°

Solution :-

Let,

One Angle = 4x.

Other Angle = 5x.

According To Question,

Third Angle = 4x + 5x = 9x.

As Per Question, Equation Formed :-

4x + 5x + 9x = 180°

➛18x = 180°

➛x = 180/18.

➛x = 10.

Now,

• First Angle = 4x = 40°

• Second Angle = 5x = 50°

• Third Angle = 9x = 90°

Hence, Correct Answer = Option [A].