Question

The diagonals of a rhombus ABCD intersect at E. Given that the measurement of angle BAC is 53, DE is 8, and EC is 6. Find the measurement of angle DAC

Answer 1

67 is the right answer

Answer 2

• The measurement of ∠DEC is equal to 53° .

Given :-

• The diagonals of a rhombus ABCD intersect at E.
• ∠BAC = 53°
• DE = 8
• EC = 6

To Find :-

• ∠DEC = ?

Concept used :-

• The diagonals of a rhombus bisect each vertex angle .

Solution :-

given that,

→ ∠BAC = 53°

now as we can see that, ∠BAC and ∠DAC are at common vertex A .

So,

→ ∠DAC = ∠BAC { since diagonals of a rhombus bisect each vertex angle }

then,

→ ∠DAC = 53° (Ans.)

Proof :- Diagonal of a rhombus bisect the vertex angle :-

In ∆DAC and ∆BAC we have,

→ DA = BA { Sides of rhombus are equal }

→ AC = AC { common }

→ DC = BC { Sides of rhombus are equal }

so,

→ ∆DAC ≅ ∆BAC { By SSS congruence rule }

then,

→ ∠DAC = ∠BAC { Corresponding parts of congruent triangles are congruent } (Proved)

Learn more :-

In the figure along side, BP and CP are the angular bisectors of the exterior angles BCD and CBE of triangle ABC. Prove ∠BOC = 90° - (1/2)∠A .

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