Question

Find the value of 'x' and 'y' respectively if ΔBAC ≅ ΔQRP

• A. 15° and 14
• B. 25° and 14
• C. 14° and 15
• D. 14° and 25

Answer 1

The correct option is B 25° and 14

Given: ΔBAC ≅ ΔQRP
We know that, when two triangles are congruent to each other, it means all angles and all sides of triangle will be equal to other triangle.
Hence, in figure ∠A = ∠R and AB = RQ

Since, ∠A = ∠R
On putting the values, we get
⇒ 2x + 15° = 5x° - 60°
⇒ 60° + 15° = 5x° - 2x°
⇒ 75° = 3x°
⇒ x° = $\frac{75°}{3}$ = 25°
⇒ x = 25

Now, AB = RQ
⇒ (3x + 10) cm = (5y + 15) cm
On putting the value x = 25, we get
⇒ (3 × 25 + 10) = (5y + 15)
⇒ (75 + 10) = (5y + 15)
⇒ 85 = (5y + 15)
⇒ 85 - 15 = 5y
⇒ y = $\frac{70}{5}$ = 14