Question

An isosceles triangle containing two angles with equal measure is shown. The degree measure of each triangle's three interior angles and an extra angle is represented with variables. Find the measure of the three interior angles 2x-18 What is the measure of angle x? What is the measure of angle y?

Answer 1

In an isosceles triangle with two angles represented by 2x-18, use the property that the sum of the interior angles is always 180 degrees to solve for x, and then find angle y.

Step-by-step explanation:

In an isosceles triangle, two angles have the same measure. The degree measure for each of the triangle's three interior angles can be found by using the fact that all triangles have interior angles adding up to 180 degrees.

If the triangle is represented with variables such as 2x-18 for each of the equal angles (base angles), then the third angle can be expressed as a function of x as well. To solve for x, we set up the equation:

2(2x - 18) + y = 180

This is because the two equal angles sum together and with the third angle y, they must equal 180 degrees. We solve for x first, then use the value of x to find the angle y.