Two angles of a triangle have equal measures, but the third angle's measure is 36° less than the sum of the other two. find the measure of each angle of the triangle. the first and second angles measure degrees, and the third angle measures degrees.

 The first and second angles measure 54 degrees, and the third angle measures 72 degrees.

Step-by-step explanation:  Given that two angles of a triangle have equal measures, but the third angle's measure is 36° less than the sum of the other two.

We are to find the measure of each angle of the triangle.

Let, x° be the measure of each of the two angles that has equal measure.

Then, the measure of the third angle will be (x° + x° - 36°) = (2x° - 36°).

From Angle-Sum-Property of a triangle, we have

So, the measure of each angle of equal measure is 54°, and the measure of the third angle is

Thus, the first and second angles measure 54 degrees, and the third angle measures 72 degrees.

(b) 240

step-by-step explanation:

first, we use the pythagorean formula using the given side lengths to find x. then we use x to find the side lengths. then we add the side lengths to find the perimeter.

pythagorean theorem formula:

a^2 + b^2 = c^2

(x - 20)^2 + (x - 40)^2 = x^2

x^2 - 40x + 400 + x^2 - 80x + 1600 = x^2

x^2 -120x + 2000 = 0

(x - 100)(x - 20) = 0

x - 100 = 0 or x - 20 = 0

x = 100 or x = 20

we see that the solution x = 20 must be discarded because it will give a negative side length and a side length of 0. the only valid solution is x = 100.

perimeter = sum of the lengths of the sides

perimeter = x + x - 20 + x - 40

perimeter = 3x - 60

replace x with 100.

perimeter = 3(100) - 60

perimeter = 300 - 60

perimeter = 240