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 20° more thantwice 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°.)
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Extra credit: Which national flag is a triangle, rather than a rectangle?
To solve this problem, let's represent the measure of the two equal angles in the isosceles triangle as x.
According to the problem, the third angle is 20° more than twice the measure of either of the other two angles. This means the third angle can be expressed as 2x + 20°.
The sum of the measures of the angles in a triangle is always 180°. So, we can add up the three angles to form an equation:
x + x + (2x + 20°) = 180°
Combining like terms, we get:
4x + 20° = 180°
Next, let's isolate x by subtracting 20° from both sides:
4x = 180° - 20°
4x = 160°
Finally, divide both sides of the equation by 4 to solve for x:
x = 160° / 4
x = 40°
The measure of each equal angle in the isosceles triangle is 40°.
To find the third angle, substitute the value of x back into the equation for the third angle:
2x + 20° = 2(40°) + 20°
2x + 20° = 80° + 20°
2x + 20° = 100°
Therefore, the measure of the third angle is 100°.
In conclusion, the measures of the angles in the isosceles triangle are 40°, 40°, and 100°.
2 x + 2 x + 20 = 180 ... x = 40
40º , 40º , 100º