How do you solve the following question?
**QRST is a rectangle. If m<QTR = 2x to the power of 2 - 7 and m<SRT = x to the power of 2 + 18, find m<QTR.
To solve this question, we need to use the properties of a rectangle.
In a rectangle, the opposite angles are equal. Therefore, we can set the measures of angle QTR and angle SRT equal to each other:
m<QTR = m<SRT
Now we can use the given information and apply it to the equation.
Given:
m<QTR = 2x^2 - 7
m<SRT = x^2 + 18
Setting them equal:
2x^2 - 7 = x^2 + 18
To solve for x, we can start by bringing all the terms to one side of the equation:
2x^2 - x^2 = 18 + 7
x^2 = 25
Now, we can take the square root of both sides to solve for x:
√(x^2) = √25
x = ±5
Since we are looking for the measure of angle QTR, we substitute the value of x into the equation for m<QTR:
m<QTR = 2x^2 - 7
m<QTR = 2(5^2) - 7
m<QTR = 2(25) - 7
m<QTR = 50 - 7
m<QTR = 43
Therefore, the measure of angle QTR is 43 degrees.