In quadrilateral QRST, m∠Q > is 68°, m∠R is (3x + 40)°, and m∠T is (5x − 52)°. What are the measures of ∠R, ∠S, and ∠T? Write the numerical values in that order with the measures separated by commas.  



To solve for the measures of angles \( \angle R \), \( \angle S \), and \( \angle T \) in quadrilateral \( QRST \), we need to use the fact that the sum of the interior angles in any quadrilateral is \( 360^\circ \).

Given:
- \( m\angle Q = 68^\circ \)
- \( m\angle R = (3x + 40)^\circ \)
- \( m\angle T = (5x - 52)^\circ \)

Let \( m\angle S = y \).

According to the sum of the interior angles of a quadrilateral:
\[
m\angle Q + m\angle R + m\angle S + m\angle T = 360^\circ
\]

Substitute the known values:
\[
68 + (3x + 40) + y + (5x - 52) = 360
\]

Simplify and combine like terms:
\[
(8x + y) + 56 = 360
\]



In quadrilateral QRST, m∠Q > is 68°, m∠R is (3x + 40)°, and m∠T is (5x − 52)°. What are the measures of ∠R, ∠S, and ∠T? Write the numerical values in that order with the measures separated by commas.

Solve for the measures of angles ∠R, ∠S, and ∠T in quadrilateral QRST, where m∠Q = 68°, m∠R = (3x + 40)°, and m∠T = (5x - 52)°. This problem covers key concepts in geometry and algebra, focusing on using the sum of angles in a quadrilateral. Suitable for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation