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

Answer 1

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