ABCD is a parallelogram in which diagonal AC bisects . if =35^ , … - Vidyadip

Question

ABCD is a parallelogram in which diagonal AC bisects $\angle\text{BAD}.$ if $\angle\text{BAC}=35^\circ,$ then $\angle\text{ABC}=$

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Answer

110°
Solution:

AC bisects $\angle\text{DAB}.$
$\Rightarrow\angle\text{DAC}=\angle\text{BAC}=35^\circ$
$\Rightarrow\angle\text{BAD}=2\times35^\circ=70^\circ$
$\angle\text{A}+\angle\text{B}=180^\circ$ (Sum of any two adjacent angles in parallelogram =180°)
$\Rightarrow\angle\text{B}=\angle\text{ABC}=180^\circ-\angle\text{BAD}$
$=180^\circ-70^\circ=110^\circ$

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