Question

the flag of a country contains an isosceles triangle (recall that an isosceles triangle contains two angles with the same measure.) if the third angle of the triangle is 20° more than twice 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°.)
the first angle is □°, the second angle is □°, and the third angle is □°.

Explanation:

Step1: Set up equations

Let the measure of the first and second angles (equal in an isosceles triangle) be \(x\), and the third angle be \(y\).
We know that \(y = 2x+ 20\) (the third - angle relationship) and \(x + x + y=180\) (sum of angles in a triangle).

Step2: Substitute and solve

Substitute \(y = 2x + 20\) into \(x + x + y=180\):

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Step3: Find the third - angle

Substitute \(x = 40\) into \(y = 2x+20\):
\(y=2\times40 + 20=80 + 20=100\)

Answer:

The first angle is \(40^{\circ}\), the second angle is \(40^{\circ}\), and the third angle is \(100^{\circ}\)