Question

In the give figure AC is parallel to DG

$\angle BED={115}^{\circ }and\angle BFG={120}^{\circ }$

Find a,b,c.

• A. $a={65}^{\circ }$ $b={55}^{\circ }$ $c={60}^{\circ }$
• B. $a={55}^{\circ }$ $b={55}^{\circ }$ $c={70}^{\circ }$
• C. $a={55}^{\circ }$ $b={65}^{\circ }$ $c={60}^{\circ }$
• D. $a={65}^{\circ }$ $b={60}^{\circ }$ $c={55}^{\circ }$

Answer 1

The correct option is A

$a={65}^{\circ }$

$b={55}^{\circ }$

$c={60}^{\circ }$

$\angle ABE+\angle BED={180}^{\circ }(Co-interiorangles.)$

$\angle ABE={180}^{\circ }-\angle BED$

$\angle ABE={180}^{\circ }-{115}^{\circ }$

$\angle ABE={65}^{\circ }$

$a={65}^{\circ }$

$\angle CBF+\angle BFG={180}^{\circ }(Co-interiorangles.)$

$\angle CBF={180}^{\circ }-\angle BFG$

$\angle CBF={180}^{\circ }-{120}^{\circ }$

$\angle CBF={60}^{\circ }$

$c={60}^{\circ }$

$a+b+c={180}^{\circ }\left(Angleinastraightline\right)$

$65+b+60={180}^{\circ }$

$b={180}^{\circ }-{125}^{\circ }$

$b={55}^{\circ }$