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Byju's Answer

Standard IX

Mathematics

Opposite Angles of a Parallelogram Are Equal

Refer the abo...

Question

Refer the above figure. The measure of $∠ C A D$ is

45^{\circ}

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35^{\circ}

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25^{\circ}

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15^{\circ}

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Solution

The correct option is B $35^{\circ}$
We know angle formed on a straight line is $180$ .
so angle $C$ will be $180$
$∠ A C B + ∠ A C D = 180$
$65 + ∠ A C D = 180$
$∠ A C D = 180 - 65 = 115$

Since sum of interior angles of a trangle is $180$
Given
$∠ C D A = 30$
$∠ C D A + ∠ C A D + ∠ A C D = 180$
$30 + ∠ C A D + 115 = 180$
$65 + ∠ A C D = 180$
$∠ C A D = 180 - (30 + 115)$
$∠ C A D = 35^{0}$

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Refer the above figure. The measure of ∠CAD is

The correct option is B 35∘We know angle formed on a straight line is 180.so angle C will be 180∠ACB+∠ACD=180 65+∠ACD=180 ∠ACD=180−65=115Since sum of interior angles of a trangle is 180Given ∠CDA=30∠CDA+∠CAD+∠ACD=180 30+∠CAD+115=18065+∠ACD=180∠CAD=180−(30+115)∠CAD=350

Refer the above figure. The measure of $∠ C A D$ is