Question

An isosceles triangle has two angles that measure 37 degrees each. Write two different equations that could be solved to find the measure of the third angle.

A. X + 106 = 180
B. 37 + X + 37 = 180

Answer 1

The student's question pertains to finding the third angle of an isosceles triangle where two angles are given as 37 degrees each. Two different equations can be formed using the fact that the sum of all angles in a triangle equals 180 degrees. Both equations, when solved, will yield the measure of the third angle.

Step-by-step explanation:

The question is based on the properties of an isosceles triangle, specifically finding the measure of the third angle given the measures of the other two angles. In an isosceles triangle, two sides are of equal length and the angles opposite those sides are also equal. The sum of the angles in any triangle is 180 degrees, and this is true for isosceles triangles as well. Given that two of the angles in the isosceles triangle are 37 degrees each, we can write two equations to find the third angle (x).

• Equation A: x + 106 = 180
• Equation B: 37 + x + 37 = 180

For Equation A, we derive 106 by adding the two known angles (37 + 37) and subtracting from 180, indicating the sum of the third angle and 106 must be equal to 180 degrees. For Equation B, we explicitly write out the sum of all three angles of the triangle. Both equations can be solved to find the measure of x, the third angle of the triangle.