Question

53. In ABC, AC = BC, S is the circumcentre and ZASB = 150°. Find angleCAB.

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Answer 1

Answer:

Draw a diagram with given condition,

Given AC=BC

thus, ∠ABC=∠BAC=55

∘

(Isosceles triangle property)

Now, in △s CDA and CDB

AC=BC (Given)

BD=AD (CD bisects AB)

CD=CD (Common side)

Hence. △CDA≅△CDB

thus, ∠BCD=∠ACD=x

∘

(Corresponding angles of congruent triangles)

Now, In △ABC,

∠ABC+∠ACB+∠BAC=180

∘

55

∘

+∠ACD+∠BCD+55

∘

=180

∘

2x

∘

=70

∘

x

∘

=35