Triangle QRS is similar to triangle FGH such that Q, R, and S correspond to F, G and H, respectively. Each side of triangle FGH has 1/4 the length of its corresponding side in triangle QRS. In triangle FGH, the measure of angle F is 35°, the measure of angle G is 8°, and FG = a. In triangle QRS, the measure of angle Q is b° and QR = 20. What is the value of a + b?

Triangle QRS is similar to triangle FGH such that Q, R, and S correspond to F, G and H... | SAT Triangles Practice

Answer: $40$

Explanation:1. Properties of similar triangles: If $\triangle QRS \sim \triangle FGH$ , then their corresponding angles are equal, and their corresponding sides are in proportion. Given correspondence: Q $\leftrightarrow$ F, R $\leftrightarrow$ G, S $\leftrightarrow$ H.

Determine the value of $b^{\circ}$ : Since $\angle Q$ corresponds to $\angle F$ , their measures are equal. $\angle F = 35^{\circ}$ . So, $\angle Q = b^{\circ} = 35^{\circ}$ . Thus, $b=35$ .
Determine the value of $a$ : Side FG in $\triangle FGH$ corresponds to side QR in $\triangle QRS$ . We are given that each side of $\triangle FGH$ has $\dfrac{1}{4}$ the length of its corresponding side in $\triangle QRS$ . So, $FG = \dfrac{1}{4} QR$ . We are given $FG=a$ and $QR=20$ . Therefore, $a = \dfrac{1}{4} \times 20$ . $a = \dfrac{20}{4}$ . $a = 5$ .
Calculate $a+b$ : $a+b = 5 + 35$ . $a+b = 40$ .

Conclusion:The value of $a+b$ is $40$ .

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