Math Problem Statement

solve b

Solve for the value of x in part (b) of the problem involving triangle PQR, with given angle ∠PRQ = 54° and unknown angle ∠QPR = x.

Solution

To solve part (b) of the problem, we need to find the value of xx in the triangle PQRPQR.

Analyzing the Triangle

  1. The triangle PQRPQR has:
    • An angle QPR=x\angle QPR = x.
    • An angle PRQ=54\angle PRQ = 54^\circ.

Since the sum of the interior angles in a triangle is always 180180^\circ, we can set up the equation:

x+54+PQR=180x + 54^\circ + \angle PQR = 180^\circ

  1. To find xx, we need to determine the missing angle PQR\angle PQR.

Solving for xx

  • Since we do not have the measurement of PQR\angle PQR, we must assume the problem requires only finding xx in terms of the other angles provided.

Using the triangle angle sum formula:

x=18054PQRx = 180^\circ - 54^\circ - \angle PQR

x=126PQRx = 126^\circ - \angle PQR

If there are any additional details about PQR\angle PQR that I missed or if you want to clarify something further, please let me know.

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Math Problem Analysis

Mathematical Concepts

Geometry
Triangle Angle Sum Theorem

Formulas

Sum of angles in a triangle = 180°

Theorems

Triangle Angle Sum Theorem

Suitable Grade Level

Grades 7-10