Question

106° 3131°439Are the figures similar?(type YES or NO)The measure of angle X=degreesThe measure of angle Y =degreesBlank 1:1Blank 2:Blank 3:

Answer 1

$\angle X+106^0+31^0=180^0(\text{Sum of angles in a triangle)}$$\begin{gathered} \angle X+137^0+180^0 \\ \angle X=180^0-137^0 \\ \angle X=43^0 \end{gathered}$

From Triangle 1,

∠X=43°

$\begin{gathered} \angle Y+31^0+43^0=180^0 \\ \angle Y+74^0=180^0 \\ \angle Y=180^0-74^0 \\ \angle Y=106^0 \end{gathered}$

From Triangle 2,

∠y=106°

Hence,

Are the figures similar? YES

∠X=43°

∠Y=106°