Finding the Angle of an Isosceles Triangle

In this problem, we are given that triangle Q R S is an isosceles triangle with base R S. We need to find the measure of angle Q.

Let's draw the triangle to visualize the situation. Since R S is the base, the two base angles R and S must be equal in measure.

The problem provides algebraic expressions for these base angles: the measure of angle R is five x minus twelve, and the measure of angle S is three x plus eighteen.

Because it is an isosceles triangle with base R S, we know the base angles are congruent. So, the measure of angle R equals the measure of angle S.

Now we solve for x. Subtract three x from both sides to combine the variables.

Next, add twelve to both sides to isolate the term with x. Eighteen plus twelve gives us thirty.

Dividing both sides by two, we find that x equals fifteen.

Now that we have x, let's find the measure of one of the base angles. Let's use angle S. Three times fifteen plus eighteen.