Question

Two angles of a triangle have the same measure and the third one is 21 degrees greater than the measure of each of the other two. Find the

measure of the largest angle in the triangle.
Answer: The largest angle has a measure of
degrees

Answer 1

Since two angles of the triangle have the same measure, the triangle is an isosceles triangle.

Let one angle be a variable (eg: x) so we can form expressions and solve.

Let the first and second angle be x°.

Form an expression for the third angle using the information given.

Third angle = (x + 21)°

Since sum of angles in a triangle is 180°, we can form an equation.

x + x + (x + 21) = 180

Simplify and solve for x.

3x + 21 = 180

3x = 159

x = 53

Largest angle is the third angle.

Substitute x into the expression to find the value.

Third angle = 53 + 21

= 74°