Question

Diagonals of a quadrilateral ABCD bisect each other. If $\angle A={35}^o$, determine $\angle B$.

• A. ${125}^o$
• B. ${135}^o$
  
• C. ${145}^o$
  
• D. ${155}^o$
  

Answer 1

The correct option is C ${145}^o$

Given -

ABCD is a quadrilateral with AC & BD as its diagonals bisecting each other at O. $\angle BAD={35}^o.$

To find out- $m\angle ABC$

Solution-

Between $\Delta AOD$ & $\Delta BOC$ we have,

$AO=CO$ & $DO=BO$ ...(since AC & BD bisect each other at O)

$\angle AOD=\angle BOC$

$\therefore \Delta AOD$ & $\Delta BOC$ are congruent. $⟹AD\parallel BC$

Now, AB is the transversal to AD & BC$

So, $\angle BAD+\angle ABD={180}^o$ ...(same side internal angles)

$⟹{35}^o+\angle ABD={180}^o$

$⟹\angle ABD={145}^o$

Ans- $\angle B={145}^o$