Question

He 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 45​° 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

27,27 and 126

Explanation:

Given that the flag of a country contains an isosceles triangle.​

Hence two angles would be congruent. Let the congruent angle be x

Now since sum of three angles of a triangle is 180, we have angles as

`x,x,180-2x`

Since third angle is 45 more than three times, we have

third angle
`= 180-2x`

45 more than three times the equal angle =
`3x+45`

So we have

`3x+45=180-2x\\5x=135\\x=27`

Third angle =
`180-2(27) =126`

So angles are 27, 27 and 126

Answer 2

The angles are 27°, 27° and 126°

let the 2 equal angles be x then the third angle = 3x + 45

sum of 3 angles = x + x + 3x + 45 = 5x + 45 = 180

hence 5x = 180 - 45 = 135⇒ x= 135/5 = 27

the angles are 27°, 27° and 3x + 45 =81 + 45 = 126°