CTET 2 Math and Science Jan 2012 Paper

Question : 39 of 120

Marks: +1, -0

In the figure, ABC is an isosceles triangle with CA = 1 CBand BC is produced to a point D. If CE⊥BC, such that ∠D

=\;\;{1}/{2}∠E=\;\;{1}/{2}∠A

Then measure of ∠ACD is

Solution:

Given that, CA = CB

∠D=\;\;{1}/{2}∠A=\;\;{1}/{2}∠E

∠{ACD}=?

In ΔCDE

x+\;\;{x}/{2}+90^{∘}=180^{∘}

⇒\;\;{3x}/{2}=90^{∘}

⇒x=\;\;{180^{∘}}/{3}⇒x=60^{∘}

180^{∘}-2x=180^{∘}-2×60^{∘}=60^{∘}

∴∠ACD=180^{∘}-∠ACB

=180^{∘}-60^{∘}=120^{∘}

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