Use app×
Join Bloom Tuition
One on One Online Tuition
JEE MAIN 2025 Foundation Course
NEET 2025 Foundation Course
CLASS 12 FOUNDATION COURSE
CLASS 10 FOUNDATION COURSE
CLASS 9 FOUNDATION COURSE
CLASS 8 FOUNDATION COURSE
0 votes
697 views
in Quadrilaterals by (23.5k points)
closed by

In a ΔABC, CA = CB. On CB square BCDE is constructed away from the triangle. If x is the number of degrees in angle DAB, then

(a) x depends upon ΔABC 

(b) x is independent of the triangle 

(c) x may equal ∠CAD 

(d) x is greater than 45° but less than 90°

1 Answer

+1 vote
by (24.0k points)
selected by
 
Best answer

(b) x is independent of the triangle 

In ΔABC, CA = CB 

⇒ ∠CBA = ∠CAB = ∠A 

∴ ∠ACB = 180° – 2∠A 

∴ ∠ACD = 180° – 2∠A + 90° 

= 270° – 2∠A 

∵ AC = AB = CD 

⇒ AC = CD 

⇒ In ΔCAD, ∠CDA = ∠CAD 

= \(\frac12\) (180° – (270° – 2∠A))  = ∠A – 45°.

= ∠A – x (∴∠CAE = ∠CAB – ∠EAB = ∠A – x) 

⇒ x = 45° So X is independent of the triangle.

Welcome to Sarthaks eConnect: A unique platform where students can interact with teachers/experts/students to get solutions to their queries. Students (upto class 10+2) preparing for All Government Exams, CBSE Board Exam, ICSE Board Exam, State Board Exam, JEE (Mains+Advance) and NEET can ask questions from any subject and get quick answers by subject teachers/ experts/mentors/students.

Categories

...