Answer:
x = 35
∠R = 35°
∠P = 20°
∠Q = 125°
Explanation:
The 3 angles in a triangle is always equal to 180 degrees.
Find the variable:
So, to find the variable, you must add all the angles together.
x + (x - 15) + (3x + 20) = 180
You can remove the parenthesis and combine variables.
x + x - 15 + 3x + 20 = 180
5x + 5 = 180
Now subtract 5 from both sides so 5x is alone.
5x = 175
Then, divide both sides by 5 so x is alone.
x = 35
To find the measures of the angles:
We know that x is equal to 35 degrees, so we can factor that into the angles.
Angle R is equal to x, so we know that is 35 degrees.
Angle P is equal to (x - 15), so we can factor the 35 degrees into the equation.
Angle P = 35 - 15 = 20 degrees
Lastly, angle Q is equal to (3x + 20), meaning we multiply 35 by 3, then add 20.
3(35) + 20
105 + 20
Angle Q = 125 degrees
You can check this by adding all the angles together and seeing if it equals 180.
35 + 20 + 125 = 180
180 = 180
Hope this helps!