It is given that ∆ABC ≅ ∆PQR, AB = 5 cm, ∠B = 40°, and ∠A = 80°. Which of the following options is true?

In a quadrilateral ABCD, E is a point in the interior of the quadrilateral such that DE and CE are the bisectors of ∠D and ∠C, respectively. If ∠B = 82° and ∠DEC = 80°, then ∠A = ?

ABC is a triangle in which DE || BC and AD: DB = 5: 4. Then DE: BC is

The sides BA and DE of a regular pentagon are produced to meet at F. What is the measure of ∠EFA?

An equilateral triangle ABC is inscribed in a circle with centre O. D is a point on the minor are BC and ∠CBD=40⁰. Find the measure of ∠BCD.

In ∆ABC, ∠C=90⁰, Point P and Q are on the sides AC and BC, respectively, such that  AP:PC=BQ:QC=1:2.Then, $${AQ^2+BP^2}\over AB^2$$  is equal to:

In a circle with centre O, BC is a chord. Points D and A are on the circle, on the opposite side of BC, such that ∠DBC = 28° and BD = DC. What is the measure of ∠BOC?

In ΔABC, D and E are points on the sides AB and AC, respectively, such that DE || BC. If AD = 5 cm, DB = 9 cm, AE = 4 cm and BC = 15.4 cm, then the sum of the lengths of DE and EC (in cm) is: