Question

triangle rst is shown below. what is the measure, in degrees, of ∠t? 35 60 70 105

Explanation:

Step1: Use the triangle - angle sum theorem

The sum of the interior angles of a triangle is \(180^{\circ}\). So, for \(\triangle RST\), we have \(x + 2x+75=180\).

Step2: Solve the equation for \(x\)

Combine like terms: \(3x+75 = 180\).
Subtract \(75\) from both sides: \(3x=180 - 75\), so \(3x = 105\).
Divide both sides by \(3\): \(x=\frac{105}{3}=35\).

Step3: Find the measure of \(\angle T\)

Since \(\angle T = 2x\), substitute \(x = 35\) into \(2x\). Then \(\angle T=2\times35 = 70^{\circ}\).

Answer:

\(70\) (the third option)