Question

If ∆ABC ≅ ∆PQR, then the value of ∠A is
(a) 35°
(b) 55°
(c) 90°
(d) 45°

​

Answer 1

Answer:

55°

Step-by-step explanation:

triangle ABC Congruent to triangle PQR by RHS criteria

line BA= line QP

line CA = line PR

(equal lines gives equal angles)

therefore , angle P = angleA

In triangle PQR

angle Q =35°

angle R = 90°

angle P = ?

angle P+ angle Q + angle R = 180° ( angle sum)

= angle P + 35 + 90 =180

= angle P+125 = 180

= angle P= 180-125

= angle P = 55°

Therefore angle P = angle A =55°

Answer 2

Given : ∆ABC ≅ ∆PQR

To Find :   value of ∠A

(a) 35°

(b) 55°

(c) 90°

(d) 45°

Solution:

∆ABC ≅ ∆PQR

Corresponding parts of congruent triangles are are congruent

Hence

AB ≅ PQ

BC ≅ QR

AC ≅ PR

∠A ≅ ∠P

∠B ≅ ∠Q

∠C ≅ ∠R

in ΔPQR

m∠P + m∠Q + m∠R = 180°

=> m∠P + 35° + 90° = 180°

=> m∠P = 55°

∠A ≅ ∠P

=> m∠A = m∠P

=>  m∠A = 55°

value of ∠A is 55°

Option b is correct

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