Question

given (\triangle rstcong\triangle lmn), (mangle r = 65^{circ}), and (mangle m = 70^{circ}), what is the measure of (angle t)? enter your answer in the box. (mangle t=square^{circ})

Explanation:

Step1: Use the property of congruent triangles

Since \(\triangle RST\cong\triangle LMN\), then \(\angle S=\angle M\). Given \(m\angle M = 70^{\circ}\), so \(m\angle S=70^{\circ}\).

Step2: Use the angle - sum property of a triangle

The sum of the interior angles of a triangle is \(180^{\circ}\). In \(\triangle RST\), we know \(m\angle R = 65^{\circ}\), \(m\angle S=70^{\circ}\). Let \(m\angle T=x\). Then \(m\angle R+m\angle S + m\angle T=180^{\circ}\), i.e., \(65^{\circ}+70^{\circ}+x = 180^{\circ}\).

Step3: Solve for \(x\)

Simplify the left - hand side of the equation: \(135^{\circ}+x=180^{\circ}\). Subtract \(135^{\circ}\) from both sides: \(x=180^{\circ}- 135^{\circ}\).

Answer:

\(45\)