Dhamaal.app
0 votes
14 views
in Plane Geometry and Line and Angle by (36.6k points)
closed by

In the figure, DE || QR and AP and BP are the bisectors of ∠EAB and ∠RBA. Find the value of ∠APB.

1 Answer

0 votes
by (35.6k points)
selected by
 
Best answer

DE || QR (given)

∴∠EAB + ∠RBA = 180°

(Sum of the interior angles on the same side of a transversal is 180°)

⇒ \(\frac { 1 }{ 2 }\)∠EAB + \(\frac { 1 }{ 2 }\)∠RBA = 90° …(i)

AP and BP are bisectors of ∠EAB and ∠RBA respectively

\(\frac { 1 }{ 2 }\)∠EAB = ∠PAB

\(\frac { 1 }{ 2 }\)∠RBA = ∠PAB

∵In ∆APB

∠PAB + ∠PBA + ∠APB = 180°

⇒ 90° + ∠APB = 180°

⇒ ∠APB = 90°

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.

...