CGL 21 Tier 2 Maths


Question 1

ABC and PQR are two triangles. AB = PQ = 6 cm, BC = QR = 10 cm and AC = PR = 8 cm. If angle ABC = x degree, then what is the value of angle PRQ? 

ABC तथा PQR त्रिभुज हैं। AB = PQ = 6 से.मी., BC = QR = 10 से.मी. तथा AC = PR = 8  से.मी. है। यदि कोण ABC = x डिग्री है, तो कोण PRQ का मान क्या है? 


Options

A

(90 - x) degree

(90 - x) degree

B

(180 - x) degree

(180 - x) degree

C

x degree

x degree

D

(90 + x) degree

(90 + x) degree


Solution:

Correct Answer:

A

(90 - x) degree

(90 - x) डिग्री


In triangles ABC and PQR

AB = PQ = 6 cm, BC = QR = 10 cm and AC = PR = 8 cm

By Side-Side-Side theorem: All three pairs of corresponding sides are equal.

We can say that triangles ABC and PQR are congruent to each other.

So corresponding angles will also be equal.

So angle ACB = angle PRQ = (90 - x) degree

ABC तथा PQR त्रिभुज में 

AB = PQ = 6 से.मी., BC = QR = 10 से.मी. तथा AC = PR = 8  से.मी.

भुजा-भुजा-भुजा प्रमेय से  : एक त्रिभुज की तीन भुजाएँ दूसरे त्रिभुज की क्रमशः तीनों संगत भुजाओं के बराबर होती हैं।

इसलिए ABC तथा PQR त्रिभुज एक दूसरे के सर्वांग्सम हो जाएँगे 

अब हम कह सकते है की तीनों संगत कोण भी बराबर होंगे ।

इसलिए कोण ACB = कोण PRQ = (90 - x) डिग्री

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