Question

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Answer 1

Answer:

(i) <BCD= 88°

(ii)<ABC =92°

Step-by-step explanation:

in a rhombus,opposite sides are parallel. So, if you take AB and CD as the parallel lines and AC as the transversal, then <CAB = <BCA=44° (opposite interior angles).

The diagonals in a rhombus intersect at 90°. in triangle COB, <BCA + <COB + <CBO=180°(angle sum property).

44° + 90° +<CBO=180°

<CBO= 180° - 134°

<CBO=46°

in triangle AOB,

<CAB + < AOB + < OBA =180°

44° + 90° + <OBA=180°

<OBA= 46°

(ii)<ABC = < CBO + < OBA = 46° + 46°=92°

<ABD = <BDC=46° (opposite interior angles)

In triangle COD,

<BDC + < DOC +<ACD=180°

46° + 90° + <ACD=180°

<ACD= 44°

(i) <BCD= <BCA + <ACD= 44° + 44°=88°

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