Point T is in the interior of ∠PQR. Find the m∠PQR if the following conditions apply. The m∠PQR = (10x - 7)°, the m∠RQT = 5x°, and the m∠PQT = (4x + 6)°
The m∠PQR is=
clearly,
10x-7 = 5x + 4x+6
x = 13
so, take it from there.
To find the measure of angle PQR (m∠PQR), you need to use the given conditions and apply the rules of angles in a triangle.
First, we know that the sum of the angles in a triangle is always 180 degrees. Using this, we can set up an equation:
m∠PQR + m∠RQT + m∠PQT = 180
Now, substitute the given values:
(10x - 7) + 5x + (4x + 6) = 180
Simplify the equation:
10x - 7 + 5x + 4x + 6 = 180
19x - 1 = 180
Add 1 to both sides:
19x = 181
Divide both sides by 19:
x = 181/19
x = 9
Now, substitute the value of x back into the equation for m∠PQR:
m∠PQR = 10x - 7
m∠PQR = 10(9) - 7
m∠PQR = 90 - 7
m∠PQR = 83
Therefore, the measure of angle PQR (m∠PQR) is 83 degrees.