Question

find and and b in the trapazium​

Answer 1

Explanation :

Construction : Extend CD from both sides.

As it is know to us that alternate interior angles are equal when two lines are parallel and a transversal cut them both. Here, CD || EG and CF is the transversal.

Also, ∠DCF and ∠GFC are the alternate interior angles. Henceforth, they'll be equal. We've been provided with the measure of ∠GFC that is 154°. So,

$\mapsto\sf{ \angle DCF = \angle GFC}$

$\mapsto \boxed{\sf{ b = 154^\circ}}$

Also, ∠DEF and ∠EDC are co-interior angles. As the sum of co-interior angles is 180°. Henceforth,

$\mapsto\sf{ \angle DEF + \angle EDC = 180^\circ}$

$\mapsto\sf{ 50^\circ + a = 180^\circ}$

$\mapsto\sf{ a = 180^\circ- 50^\circ}$

$\mapsto \boxed{\sf{ a = 130^\circ}}$

∴ The value of a is 130° and the value of b is 154°.

$\rule{200}2$

Answer 2

A is 130
B is 154
…. Thanks…….