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$A B C D$ is a parallelogram in which diagonal $A C$ is a parallelogram in which diagonal bisects $∠ B A D$ bisects . If $∠ B A C = 35 °$ . If , then the value of $∠ A B C$ , then the value of from the following choices is:

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70 °

110 °

90 °

120 °

answer is B.

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Detailed Solution

It is given that,

A B C D

is a parallelogram in which diagonal

A C

bisects

∠ B A D

∠ B A C = 35 °

Construct a parallelogram

A B C D

Calculate the measure of

∠ B A D

.
From the diagram,

∠ B A D = ∠ B A C + ∠ D A C ∠ B A D = 35 ° + 35 ° ∠ B A D = 70 ° … … .. (2)

Calculate the value of

∠ A B C .

The adjacent angles of a parallelogram are supplementary. So,

∠ A B C + ∠ B A D = 180 °

.
From (2),

∠ A B C + ∠ B A D = 180 ° 70 ° + ∠ A B C = 180 ° ∠ A B C = 110 °

The value of

∠ A B C

110 °

.
Hence, option 2) is correct.

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