Question

1. what is m∠rts in the triangle below?

(4x + 11)° at r, 43° at s, (7x - 6)° at t.
options: a. 59° b. 75° c. 78° d. 81°

Explanation:

Step1: Recall Triangle Angle Sum

The sum of angles in a triangle is \(180^\circ\). So, \((4x + 11)^\circ+(7x - 6)^\circ + 43^\circ=180^\circ\).

Step2: Simplify the Equation

Combine like terms: \(4x + 7x+11 - 6 + 43 = 180\) → \(11x + 48 = 180\).

Step3: Solve for \(x\)

Subtract 48 from both sides: \(11x = 180 - 48 = 132\). Divide by 11: \(x=\frac{132}{11}=12\).

Step4: Find \(m\angle RTS\)

\(\angle RTS\) is \((7x - 6)^\circ\). Substitute \(x = 12\): \(7(12)-6=84 - 6 = 78^\circ\).

Answer:

C. \(78^\circ\)