Question

given congruent triangles, solve for the variable.
9
a
65°
b
f
d
c
e
k
r
65°
45°
o
m
v
t
y=
y=

Explanation:

Step1: First triangle pair

• Use triangle angle - sum property ($180^{\circ}$ in a triangle).
• In $\triangle ABC$, $\angle A = 65^{\circ}$, $\angle C=90^{\circ}$. Then $\angle B=180^{\circ}-(90^{\circ} + 65^{\circ})=25^{\circ}$.
• Since $\triangle ABC\cong\triangle DEF$, $\angle E=\angle B$. So $y = 25$.

Step2: Second triangle pair

• Use triangle angle - sum property ($180^{\circ}$ in a triangle).
• In $\triangle RVT$, $\angle R = 45^{\circ}$.
• Since $\triangle OKM\cong\triangle RVT$, $\angle O=\angle V = 65^{\circ}$. Then $y=180^{\circ}-(45^{\circ}+65^{\circ}) = 70$.

Answer:

$25$; $70$