△GHI∼△LKJ

Question

, and m∠G=30°
, m∠H=80°
, and m∠I=70°
. What are the measures of angles J
, K
, and L

Answer 1

Since the triangles $\mathrm{△}GHI$ and $\mathrm{△}LJK$ are similar (indicated by $\mathrm{△}GHI\sim \mathrm{△}LJK$), the corresponding angles of the two triangles are equal.

Given:

• $m\mathrm{\angle }G={30}^{\circ }$
• $m\mathrm{\angle }H={80}^{\circ }$
• $m\mathrm{\angle }I={70}^{\circ }$

First, let's verify that the angles in $\mathrm{△}GHI$ sum to ${180}^{\circ }$:

$$m\mathrm{\angle }G+m\mathrm{\angle }H+m\mathrm{\angle }I={30}^{\circ }+{80}^{\circ }+{70}^{\circ }={180}^{\circ }$$

Now, since the triangles are similar, we can determine the angles in $\mathrm{△}LJK$:

1. $m\mathrm{\angle }L=m\mathrm{\angle }G={30}^{\circ }$
2. $m\mathrm{\angle }J=m\mathrm{\angle }H={80}^{\circ }$
3. $m\mathrm{\angle }K=m\mathrm{\angle }I={70}^{\circ }$

Thus, the measures of angles $J$, $K$, and $L$ are as follows:

• $m\mathrm{\angle }L={30}^{\circ }$
• $m\mathrm{\angle }J={80}^{\circ }$
• $m\mathrm{\angle }K={70}^{\circ }$