ICSE Class X Math 2014 Solved Paper

In the figure, $\∠D B C=58° . B D$ is a diameter of the circle. Calculate:

Question : 13 of 52

Marks: +1, -0

∠ B D C

Solution:

△ {\BCD} ; ∠ {\DBC}=58^{∘}

(given)

∠ {\BCD}=90^{∘}

(Angle in the semicircle as

{\BD}

is diameter)

\; ∴ ∠ {\DBC}+∠ {\BCD}+∠ {\BDC}=180^{∘}

\;58^{∘}+90^{∘}+∠ {\BDC}=180^{∘}

\;⇒ \;\; ∠ {\BDC}=180^{∘}- (90^{∘}+58^{∘})

\;\; = 180^{∘}-148^{∘}=32^{∘}

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