Question

44
ABC is a triangle in which AB = AC as shown in the figure. The base BO
produced to D and the LACD = 130°. What is the measure of ZA?
A
1300
B
C.
(a) 90°
(b) 60°
(c) 80°
(d) 160°​

Answer 1

Given,

AB = AC.

∴∠ABC = ∠ACB

(angles opposite to equal sides of a triangles are equal)

∠ACD =130° (given)

∠ACB = 180° − 130° = 50° [linear pair]

⟹ ∠ABC = ∠ACB = 50°

∴∠A = 180° − (∠ABC + ∠ACB)

∠A = 180° − (50° + 50°)

Hence,

∠A = 80°

Option (c) 80° is correct.

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