Question

$\text{In the given figure, if AB}\parallel \text{CD, l is a transversal}$
$\text{and}\angle 1={65}^{\circ },\text{then the sum of}\angle 3,\angle 5,and\angle 8$
$\text{is \_\_\_}.$

• A. ${195}^{\circ }$
• B. ${295}^{\circ }$
• C. ${245}^{\circ }$
• D. ${345}^{\circ }$

Answer 1

The correct option is C ${245}^{\circ }$


$\text{Given: AB}\parallel \text{CD and}\angle 1={65}^{\circ }$

$\therefore \angle 5=\angle 1={65}^{\circ }\text{(Corresponding angles)}$

$\text{And,}\angle 8=\angle 5={65}^{\circ }\text{(Vertical angles)}$

$\text{Also,}\angle 3+\angle 5={180}^{\circ }$
$\text{(As they are interior angles on the same side}$
$\text{of transversal)}$

$\text{So, the value of}\angle 3+\angle 5+\angle 8is:$
$={180}^{\circ }+{65}^{\circ }$
$={245}^{\circ }$

Hence, option 'c' is the correct answer.