 # Write the triangle similarity statement and the reason for why the triangles \triangle XYZ\sim \triangle ? By: ? are similar. Ernstfalld 2021-08-11 Answered
Write the triangle similarity statement and the reason for why the triangles are similar. $$\displaystyle\triangle{X}{Y}{Z}\sim\triangle?{B}{y}:?$$

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Step 1
Taking $$\displaystyle\triangle{X}{Y}{Z}$$
$$\displaystyle\angle{X}={45}^{{\circ}},\angle{Y}={85}^{{\circ}}$$
Now,
Since sum of interior angle of triangle is $$\displaystyle{180}^{{\circ}}$$
$$\displaystyle\Rightarrow\angle{X}+\angle{Y}+\angle{Z}={180}^{{\circ}}$$
$$\displaystyle{45}^{{\circ}}+{85}^{{\circ}}+\angle{Z}={180}^{{\circ}}$$
$$\displaystyle\angle{Z}={180}^{{\circ}}-{130}^{{\circ}}$$
$$\displaystyle\angle{Z}={50}^{{\circ}}$$
Step 2
Taking $$\displaystyle\triangle{W}{Y}{U}$$
$$\displaystyle\angle{W}={50}^{{\circ}},\angle{Y}={85}^{{\circ}}$$
Now,
Since sum of interior angle of triangle is $$\displaystyle{180}^{{\circ}}$$
$$\displaystyle\Rightarrow\angle{W}+\angle{Y}+\angle{U}={180}^{{\circ}}$$
$$\displaystyle{50}^{{\circ}}+{85}^{{\circ}}+\angle{U}={180}^{{\circ}}$$
$$\displaystyle\angle{U}={180}^{{\circ}}-{135}^{{\circ}}$$
$$\displaystyle\angle{U}={45}^{{\circ}}$$
Step 3
In $$\displaystyle\triangle{X}{Y}{Z}\ {\quad\text{and}\quad}\ \triangle{U}{Y}{W}$$
$$\displaystyle\angle{X}=\angle{U}={50}^{{\circ}}$$
$$\displaystyle\angle{Y}=\angle{Y}={85}^{{\circ}}$$
$$\displaystyle\angle{Z}=\angle{W}={45}^{{\circ}}$$
Therefore
$$\displaystyle\triangle{X}{Y}{Z}\sim\triangle{U}{Y}{W}$$ By: AA similarity