Question

The largest and the second largest angles of a triangle are in the ratio of 3:2 respectively. The
smallest angle is 20% of the sum of the largest and the second largest angles. What is the sum
of the smallest and the second largest angles?
a) 80˚ b) 60˚ c) 100˚ d) 90˚ e) None of these

Answer 1

the ratio of largest and second largest is 3:2
let smallest to be y
let largest to be 3x
let second largest to be 2x
$y + 3x + 2x = 180$

Answer 2

Answer:

90°

Step-by-step explanation:

We are give that The largest and the second largest angles of a triangle are in the ratio of 3:2 respectively.

Let the ratio be x

Largest angle = 3x

Second largest angle = 2x

Let the smallest angle be y

Now we are given that  The smallest angle is 20% of the sum of the largest and the second largest angles.

$y=\frac{20}{100}(3x+2x)$

$y=\frac{20}{100}(5x)$

$y=\frac{1}{5}(5x)$

$y=x$

Now using angle sum property of triangle

$x+3x+2x=180$

$6x=180$

$x=30$

Smallest angle = 30°

Second largest angle = 2x = 2(30)=60°

Sum of the smallest and the second largest angles = 30°+60° = 90°

Hence Sum of the smallest and the second largest angles is  90°