QuestionFind the angle measures of a triangle where , , .
Studdy Solution
STEP 1
Assumptions1. The measure of angle is
. The measure of angle Q is
3. The measure of angle R is
4. The sum of the measures of the angles in a triangle is
STEP 2
First, we need to set up an equation that represents the sum of the measures of the angles in the triangle. This equation is the sum of the measures of angle, Q, and R equals .
STEP 3
Now, plug in the given expressions for the measures of the angles, Q, and R.
STEP 4
implify the left side of the equation by combining like terms.
STEP 5
Calculate the sum of the terms.
STEP 6
Subtract from both sides of the equation to isolate the term with the variable on the left side.
STEP 7
Calculate the right side of the equation.
STEP 8
Divide both sides of the equation by $$ to solve for $x$.
STEP 9
Calculate the value of .
STEP 10
Now that we have the value of , we can substitute it into the expressions for the measures of the angles to find their degree measures.
For angle
STEP 11
Substitute into the expression for .
STEP 12
Calculate the degree measure of angle.
STEP 13
For angle Q
STEP 14
Substitute into the expression for .
STEP 15
Calculate the degree measure of angle Q.
STEP 16
For angle R
STEP 17
Substitute into the expression for .
STEP 18
Calculate the degree measure of angle R.
The degree measures of the angles in the triangle are , , and .
Was this helpful?