Question

please solve fast . its emergence ​

Answer 1

Given:

• Three straight lines AB, CD, and EF intersects at point O.
• $\sf \angle \: COE = 45\degree \: \: \: and \: \: \: \angle AOF = 90 \degree$

To find:

• $\sf \angle BOD$

Concept used:

• Vertically opposite angles are equal.
• Sum of all angles in a straight line at the same point is always equal to 180°.

Solution:

Please note that,

$\sf \angle COE \: \: and \: \: \angle DOF \: are \: vertically \: opposite \: angles.$

$\sf \therefore \angle COE = \angle DOF$

But,

$\sf \angle COE = 45 \degree$

$\sf \therefore \angle DOF = 45 \degree$

Now, note that:

$\sf \angle AOF + \angle DOF + \angle BOD = 180 \degree$

$\sf but \\ \angle AOF = 90 \degree \\ \angle DOF = 45 \degree$

$\sf \therefore 90 \degree + 45 \degree + \angle BOD = 180 \degree$

$\sf \implies 135 \degree + \angle BOD = 180 \degree$

$\sf \implies \angle BOD = 180 \degree - 135 \degree$

$\sf \implies \angle BOD = 45 \degree$

$\huge \boxed{ \sf Hence, \: x = 45 \degree}$