If m<PQR=(10x-7),m<RQT=5x, and m<PQT=(4x=6)
455
I see that you have provided some information about the measures of angles in a triangle:
- The measure of angle PQR is given as 10x - 7.
- The measure of angle RQT is given as 5x.
- The measure of angle PQT is given as 4x + 6.
To find the values of x and the measures of the angles PQR, RQT, and PQT, we can use the fact that the sum of the angles in a triangle is always 180 degrees.
So, let's set up an equation to represent this:
(10x - 7) + (5x) + (4x + 6) = 180
To solve for x, we will combine like terms and isolate x:
10x + 5x + 4x - 7 + 6 = 180
19x - 1 = 180
19x = 180 + 1
19x = 181
x = 181/19
x ≈ 9.53
Now, we can substitute this value of x back into the given expressions to find the measures of the angles:
- Measure of angle PQR = 10x - 7 = 10(9.53) - 7 ≈ 95.3 - 7 ≈ 88.3 degrees.
- Measure of angle RQT = 5x = 5(9.53) ≈ 47.65 degrees.
- Measure of angle PQT = 4x + 6 = 4(9.53) + 6 ≈ 38.12 + 6 ≈ 44.12 degrees.
So, the measure of angle PQR is approximately 88.3 degrees, the measure of angle RQT is approximately 47.65 degrees, and the measure of angle PQT is approximately 44.12 degrees.