Question

question
in δstu, m∠s = (9x + 7)°, m∠t = (5x − 2)°, and m∠u = (x + 10)°. find m∠u.

answer attempt 1 out of 2

m∠u = ° submit answer

Explanation:

Step1: Use the triangle angle - sum theorem

The sum of the interior angles of a triangle is \(180^{\circ}\). So, \((9x + 7)+(5x - 2)+(x + 10)=180\).

Step2: Simplify the left - hand side of the equation

Combine like terms: \((9x+5x + x)+(7 - 2+10)=180\), which gives \(15x+15 = 180\).

Step3: Solve for \(x\)

Subtract \(15\) from both sides: \(15x=180 - 15=165\). Then divide both sides by \(15\): \(x=\frac{165}{15}=11\).

Step4: Find \(m\angle U\)

Substitute \(x = 11\) into the expression for \(m\angle U\). Since \(m\angle U=(x + 10)^{\circ}\), then \(m\angle U=(11 + 10)^{\circ}=21^{\circ}\).

Answer:

\(21\)