In an isosceles triangle, one angle is 24° more than twice the measure of one of the equal angles. Find the measure of each angle.

Question

In an isosceles triangle, one angle is 24° more than twice the measure of one of the equal angles. Find the measure of each angle.

 ° (smaller angle)

 ° (smaller angle)

 ° (larger angle)

Answer 1

let one of the equal angle of isosceles triangle is x degree

Then according to question one angle is 24 degree more then twice of the equal angle

so one angle = 2*x+24

As we know the sum of all angles of a triangle=180 degree

so x + x + (2*x+24)=180

4x = 180-24

x = 156/4= 39 degree

so the smaller angle = 39 degree

smaller angle = 39 degree

Larger angle = 2*x+24 = 2*39+24 = 102 degree

Answer 2

Let two equal angles be 'b

And other angle be 'a'

So, a=24 + 2b {Since, one angle is 24 degrees more than twice the measure of one of the equal angles }

We know that, Sum of angles in a triangle is 180 degrees.

So, a + b + b = 180 degrees

24 + 2b + b + b = 180 degrees

24 + 4b = 180

4b = 180 - 24

4b = 156

b = 39 degrees

Substitute in a=24+2b

a=24+2(39)

a=24+78

a=102 degrees

° (smaller angle) = 39

 ° (smaller angle) = 39

 ° (larger angle)= 102