Question

δghi ~ δrts. what are m∠g and m∠h?
(there are two triangles, δghi with angle at i being 75°, and δrts with angle at t being 55° and angle at r being 50°)
m∠g = \boxed{\space}°
m∠h = \space °

Explanation:

Step1: Use the property of similar triangles

Since \(\triangle GHI\sim\triangle RTS\), corresponding angles are equal. \(\angle G\) corresponds to \(\angle R\). So \(m\angle G = 50^{\circ}\)

Step2: Use the angle - sum property of a triangle

The sum of angles in a triangle is \(180^{\circ}\). For \(\triangle GHI\), we know \(m\angle I=75^{\circ}\), \(m\angle G = 50^{\circ}\). Let \(m\angle H=x\). Then \(x+75^{\circ}+50^{\circ}=180^{\circ}\)

$$x=180^{\circ}-(75^{\circ} + 50^{\circ})$$

$$x=180^{\circ}-125^{\circ}$$

$$x = 55^{\circ}$$

Answer:

\(m\angle G = 50^{\circ}\), \(m\angle H=55^{\circ}\)