Question

the two triangles below are similar. also, ( mangle z = 20^{circ} ) and ( mangle y = 90^{circ} ) as shown below. find ( mangle g ), ( mangle h ), and ( mangle i ). assume the triangles are accurately drawn. ( mangle g=square^{circ} ) ( mangle h=square^{circ} ) ( mangle i=square^{circ} )

Explanation:

Step1: Use the property of similar triangles

Similar triangles have equal corresponding angles. So, \(m\angle G=m\angle Z = 20^{\circ}\), \(m\angle I=m\angle Y = 90^{\circ}\).

Step2: Use the angle - sum property of a triangle

The sum of the interior angles of a triangle is \(180^{\circ}\). For \(\triangle GHI\), we know \(m\angle G + m\angle H+m\angle I=180^{\circ}\). Substitute \(m\angle G = 20^{\circ}\) and \(m\angle I = 90^{\circ}\) into the formula: \(20^{\circ}+m\angle H + 90^{\circ}=180^{\circ}\). Then \(m\angle H=180^{\circ}-(20^{\circ}+90^{\circ}) = 70^{\circ}\).

Answer:

\(m\angle G = 20^{\circ}\), \(m\angle H = 70^{\circ}\), \(m\angle I = 90^{\circ}\)