Question

If ∆ABC is congruent to ∆PQR and ∠CAB = 65°, then ∠RPQ is *
a) 65°
(b) 75°
(c) 90°
(d) 115

Answer 1

Answer:

65

Step-by-step explanation

It is given that they are congruent which means corresponding parts are equal

CAB is corresponding to RPQ

therefore CAB=RPQ=65

Answer 2

Given:

∆ABC ≅ ∆PQR

∠CAB = 65°

To find:

∠RPQ =?

Solution:

• It is given that the ∆ABC is congruent to ∆PQR.
• This implies that the angles that are corresponding in both the triangles are equal or identical to each other.
• Also, the sides that are corresponding in triangles are identical to each other.

Identical angles are as follows:

=> ∠A = ∠P

=> ∠B = ∠Q

=> ∠C = ∠R

Identical sides are as follows:

=> AB = PQ

=> BC = QR

=> AC = PR

=> ∠CAB = ∠A = 65°

=> But ∠A = ∠P = ∠RPQ

∴ ∠RPQ = 65° (measure of angles are similar due to congruency rule)

Hence, the measure of ∠RPQ is 65° (option a).