Question

in the figure BD equal DC and angle DBC is equal to 25 degree find the measure of BAC angle

Answer 1

Given that - BD = DC. This implies that angle DBC = angle DCB.

angle DBC = angle DCB = 25.

angle D = 180 -50 = 130.

Since ABCD is a cyclic quadrilateral,

                           

                                angle BDC + angle BAC = 180.

                                                    angle BAC = 180 - 130

                                                                    = 50

Answer 2

BD = DC.         ( given)

∠ DBC = ∠ DCB.                ( angles opposite to equal sides )

∴∠ DBC = ∠DCB = 25.

In Δ BDC,

∠ DBC =25° ∠DCB = 25°.

we have to find out ∠D or ∠ BDC?

∠ DBC + ∠DCB + ∠ BDC+ 180°

∠BDC = (180° -50°) = 130°.

From the property of circle, we know that angle subtended by same chord  on the minor segment is twice the angle on major segment.

Hence , 2 ∠BAC = ∠BDC= ∠BAC=( $\frac{130}{2}$ )= 65°

Ans :-  the measure of BAC angle will be 65°.

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