Question

A triangle has two of its angles ${80}^{\circ }$ and ${60}^{\circ }$. Find any two angles of a triangle which is similar to the given triangle.

• A. ${80}^{\circ },{80}^{\circ }$
• B. ${60}^{\circ },{60}^{\circ }$
• C. ${60}^{\circ },{40}^{\circ }$
• D. ${80}^{\circ },{50}^{\circ }$

Answer 1

The correct option is C ${60}^{\circ },{40}^{\circ }$

Sum of angles of a triangle $={180}^{\circ }$
If two angles are ${80}^{\circ }$ and ${60}^{\circ }$, then third angle is ${180}^{\circ }-{80}^{\circ }-{60}^{\circ }={40}^{\circ }.$
Thus, the angles of the gives traingles are ${80}^{\circ }$, ${60}^{\circ }$ and ${40}^{\circ }$.

Any triangle with two of these 3 angles is similar to the given triangle according to AA similarity criteria.