Question

in CAT the measure of the largest angle is 10 less than 5 time the smallest angle. The measure of the middle angle is 6 more than twice the measure of the largest ANGLE. wHAT IS THE MEASURE OF THE MIDDLE ANGLE?

Answer 1

The measure of middles angle is 113.5° .

Explanation:

Given as :

The measure of the largest angle is 10 less than 5 time the smallest angle.

The measure of the middle angle is 6 more than twice the measure of the largest angle

Let The largest angle = L

Let The middle angle = M

Let The smallest angle = S

As per statement

Largest angle = 5 times smallest angle - 10

i.e L = 5 × S - 10 .....1

Again

Middle angle = twice largest angle + 6

i.e M = 2 × L + 6 ......2

Since for any Triangle sum of three angles = 180°

i.e ∠L + ∠M + ∠S = 180°

Or, ( 5 × S - 10 ) + ( 2 × L + 6 ) + S = 180°

Or, ( 5 × S - 10 ) + [ 2 × (5 × S - 10 ) + 6 ] + S = 180°

Or, 5 S - 10 + (10 S - 20 + 6) + S = 180°

Or, 5 S - 10 + 10 S - 20 + 6 + S = 180°

Or, (5 + 10 + 1) S - 24 = 180°

Or, 16 S = 180° + 24

Or, 16 S = 204

∴ S =
`(204)/(16)`

i.e S = 12.75

So, The measure of smallest angle = S = 12.75°

And

L = 5 × 12.75 - 10

i.e L = 53.75

So, The measure of Largest angle = L = 53.75°

And

M = 2 × L + 6

Or, M = 2 × 53.75 + 6

i.e M = 107.5 + 6 = 113.5

So, The measure of middles angle = M = 113.5°

Hence, The measure of middles angle is 113.5° . Answer