Question

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 _____° more than three times 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 _____°.

Answer 1

The measure of each of the other two angles in the isosceles triangle is 15° and the measure of the third angle is 60°.

Step-by-step explanation:

The measure of the third angle in an isosceles triangle is = 3x + x+? where x is the measure of each of the other two angles. The sum of the measures of the angles in a triangle is always 180°.

Let's solve for x in terms of the third angle:

• Let x be the measure of each of the other two angles.
• Then, the measure of the third angle is 3x + x+?
• We can write an equation using the sum of the measures of angles in a triangle: 3x + x + (3x + x+?) = 180°
• Combine like terms: 8x + 2x+? = 180°
• Simplify the equation: 10x + 2x+? = 180°
• Combine like terms: 12x+? = 180°
• Solve for x: x = 180°/12
• Simplify: x = 15°//li>

Therefore, the measure of each of the other two angles is 15°.

The measure of the third angle is 3(15°) + 15°+? = 45° + 15° = 60°.

So, in this isosceles triangle, each of the other two angles measures 15° and the third angle measures 60°.

Learn more about Angles in a Triangle