The third angle in an isosceles triangle is 56° more than twice as large as each of the two base angles. Find the measure of each angle.
Let x = each of the other two angles, then the third angle = x + 56º
x + x + (x+56º) = 180º
Solve for x.
In re-reading your problem, third angle = 2x + 56º.
Sorry.
To find the measure of each angle in the isosceles triangle, we can start by identifying the given information:
1. We know that an isosceles triangle has two base angles that are congruent.
2. The third angle in the triangle is 56° more than twice as large as each of the base angles.
Let's assume that each base angle measures x degrees.
Based on the information given, we can express the relationship among the angles using equations:
1. The sum of the three angles in any triangle is 180°:
x + x + (2x + 56) = 180
2. The base angles of an isosceles triangle are congruent:
x = x
Now, let's solve the equation to find the value of x and then determine the measure of each angle:
2x + x + 56 = 180
3x + 56 = 180
3x = 180 - 56
3x = 124
x = 124/3
x ≈ 41.33
Now that we have the measure of x, we can calculate the measure of the other angles:
The base angles are approximately 41.33° each.
The third angle is 2(41.33) + 56 = 83 + 56 = 139°.
So, the measure of each angle in the isosceles triangle is approximately:
Base Angles: 41.33° each
Third Angle: 139°