In the figure given below A 80oand ABC 60o BD and CD bisect angles Band C respectively What are the ...........

Quantitative Aptitude (CDS) Coordinate Geometry

In the figure given below, $\small \angle$ A = 80^oand $\small \angle$ ABC = 60^o . BD and CD bisect angles Band C respectively. What are the values of X and Y respectively?

10 and 130

10 and 125

20 and 130

20 and 125

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Explanation:

In triangle ABC
$\small \angle$ A + $\small \angle$ ABC + $\small \angle$ BCA = 180^o
=> 80^o + 60^o + 2x^o = 180^o
=> 2x^o = 180^o - 140^o
=> x^o = 40^o/ 2 = 20^o
$\small \angle$ CBD = 60^o / 2 = 30^o ( As BD is an angle bisector of $\small \angle$ ABC)
In triangle BCD:
$\small \angle$ CBD + y^o + x^o = 1800
=>y^o = 1800 – 300 – 200 = 1300
Hence, x^o = 200 and y^o = 1300