Question

What is m≤PQR if PQR is (3x-6) and RQS is (x+2)?

Answer 1

To find the measurement of angle PQR, additional context is required to determine the relationship between angles PQR and RQS. Assuming they are supplementary, the equation to solve is (3x-6) + (x+2) = 180, which will allow calculation of m<=PQR.

Step-by-step explanation:

The student is asking to find the measurement of angle PQR given the expressions for angles PQR and RQS. In this context, it's important to know if these angles are adjacent and form a straight line, or lie within a triangle or another geometrical figure to provide a precise answer. Without additional context, it's not possible to determine the exact value of m≤PQR just based on these two expressions. However, if we assume that PQR and RQS form a straight line (which means they are supplementary), we can set up the equation (3x - 6) + (x + 2) = 180. This is because supplementary angles add up to 180 degrees. Solving this equation for x will allow us to find the measurement of angle PQR.

Answer 2

The m∠PQR if ∠PQR is (3x - 6) and ∠RQS is (x + 2) is 320°.

Step-by-step explanation:

If line PS has midpoint Q and ray QR, then line PQS will be a straight line, and ∠PQR + ∠RQS = 180 (sum of angles on a straight line). Given ∠PQR = 3x - 6 and ∠RQS = x + 2, to get x, we will use the relationship above:

(3x - 6) + (x + 2) = 180

4x - 4 = 180

Add 4 to both sides:

4x - 4 + 4 = 180 + 4

4x = 184

x = 184/4

x = 46

Since ∠PQR = 3x - 6, we substitute the value of x into the formula:

∠PQR = 3x-6

∠PQR = 3(46) - 6

∠PQR = 138 - 6

∠PQR = 132°

Hence, the size of the angle PQR is 132°.

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