The measures of the angles of triangle PQR can be represented in terms of x: The measure of angle P is (2x). The measure of angle Q is (x+17). The measure of angle R is (x-21) Create and solve an equation to find the measure of each angle
To find the measures of the angles, we need to set up an equation using the fact that the sum of the angles in a triangle is equal to 180 degrees.
So, we can write the equation as:
(2x) + (x + 17) + (x - 21) = 180
Simplifying the equation:
2x + x + 17 + x - 21 = 180
Combining like terms:
4x - 4 = 180
Adding 4 to both sides:
4x = 184
Dividing both sides by 4:
x = 46
Now we can substitute the value of x back into the expressions for each angle to find their measures:
Angle P = 2x = 2(46) = 92 degrees
Angle Q = x + 17 = 46 + 17 = 63 degrees
Angle R = x - 21 = 46 - 21 = 25 degrees
Therefore, the measure of each angle is:
Angle P: 92 degrees
Angle Q: 63 degrees
Angle R: 25 degrees