Question

The flag of a country contains an isosceles triangle.​ (Recall that an isosceles triangle contains two angles with the same​ measure.) If the measure of the third angle of the triangle is 25​° more than three times nbsp the measure of either of the other two​ angles, find the measure of each angle of the triangle.​ (Recall that the sum of the measures of the angles of a triangle is​ 180°.)

Answer 1

31 degrees, 31 degrees, 118 degrees

Step-by-step explanation:

Step 1 :

Let x be the measure of 2 angles of the given isosceles triangle with same measure

Let y be the measure of  3rd angle

So we have x + x + y = 180

Step 2 :

Given that the measure of  3rd angle of  triangle is 25​° more than three times the measure of either of the other two​ angles

So we have , y = 3 x + 25

Step 3:

Substituting for y in the first equation we have,

x + x + 3 x + 25 = 180

=> 5 x + 25 = 180

=> 5 x = 180-25 = 155

=> x = 155/5 = 31

Hence the 2 angles of the triangle are 31 degrees.

Step 4:

we have y = 3 x + 25

=> y = 3 * 31 + 25 = 118

Hence the 3rd angle of given triangle is 118 degrees