Find m∠RQT if m∠PQR = (10x – 9) °, m∠RQT = (5x) °, and m∠PQT = (2x + 6) °
m∠PQR= degree
If QR divides ∠PQT, then
10x-9 + 5x = 2x+6
If QT divides ∠PQR, then
10x-9 = 5x + 2x+6
Since you did not describe the figure, you must decide which case holds. In any case, clearly, one angle is the sum of the other two, so just do the math.
To find the measure of angle RQT, we can use the fact that the sum of the angles in a triangle is 180 degrees.
In this case, we are given the measures of angles PQR, RQT, and PQT. We can set up an equation based on the sum of these angles:
PQR + RQT + PQT = 180
Substituting the given angle measures:
(10x - 9) + (5x) + (2x + 6) = 180
Simplifying the equation:
10x - 9 + 5x + 2x + 6 = 180
17x - 3 = 180
Adding 3 to both sides:
17x = 183
Dividing both sides by 17:
x = 183/17 ≈ 10.7647
Now that we have the value of x, we can substitute it back into the expression for angle RQT to find its measure:
m∠RQT = 5x
m∠RQT = 5(10.7647)
m∠RQT ≈ 53.82353 degrees
So, the measure of angle RQT is approximately 53.82353 degrees.