Question

△fgh ~ △dce. what are m∠c and m∠h?
f
35°
c
d
g
50°
h
e
85°
m∠c = \\(\square\\)°
m∠h = \\(\square\\)°

Explanation:

Step1: Use the property of similar triangles

Since \(\triangle FGH\sim\triangle DCE\), corresponding angles are equal. \(\angle C\) corresponds to \(\angle F\), so \(m\angle C = 35^{\circ}\).

Step2: Use the angle - sum property of a triangle

In \(\triangle FGH\), we know that the sum of angles in a triangle is \(180^{\circ}\). Given \(\angle F = 35^{\circ}\) and \(\angle G=57^{\circ}\). Let \(m\angle H=x\). Then \(35 + 57+x=180\).

$$x=180-(35 + 57)=180 - 92=88^{\circ}$$

Since \(\angle H\) corresponds to \(\angle E\) (because of similar triangles \(\triangle FGH\sim\triangle DCE\)), \(m\angle H = 88^{\circ}\)

Answer:

\(m\angle C = 35^{\circ}\), \(m\angle H=88^{\circ}\)