Question

40° In Figure 9, ABCD is a rhombus in which ZABD Find i. ZBAC ii. ZBCD iii. ZADC.​

Answer 1

Answer:

From the figure it is given that, ABCD is a rhombus∠ABD=50

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(i) Consider the △AOB, We know that, sum of measures of interior angles of triangle is equal to 180

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∠OAB+∠BOA+∠ABO=180

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∠OAB+90

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+50

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=180

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By transposing we get,

∠OAB+140

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=180

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∠OAB=180

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−140

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∠OAB=40

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Therefore, ∠CAB=40

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(ii) ∠BCD=2∠ACD

=2×40

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=80

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(iii) Then, ∠ADC=2∠BDC

∠ABD=∠BDC because alternate angles are equal

=2×50

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=100

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