Question

Q6. AABC Z APQR, find the values of'a' and 'b.
A
R
b + 5)
Ca - 10)
B
С​

Answer 1

ΔABC ≅ ΔPQR

So, by CPCT;

• ∠A = ∠P
• ∠B = ∠Q
• ∠C = ∠R

Since,

∠A = ∠P,

⇒ (b + 5)° = 55°

⇒ b = 55° - 5°

∴ b = 50°

Now, In ΔABC,

By Angle Sum Property,

∠A + ∠B + ∠C = 180°

⇒ (b + 5) + 90° + ∠C = 180°

⇒ (50 + 5) + 90° + ∠C = 180°

⇒ 55° + 90° + ∠C = 180°

⇒ 145° + ∠C = 180°

⇒ ∠C = 180° - 145°

∴ ∠C = 35°

Since ∠B = ∠Q,

(a - 10)° = 90°

⇒ a = 90° + 10°

∴ a = 100°

Know more:

• Angle Sum Property states that Sum of all angles in a Triangle is 180°
• CPCT or Corresponding Sides of Congruent Triangles states that in 2 congruent triangles, the corresponding sides and angles are equal.