Angle A=6x-35° Angle B=3x+53° Solve for x then find the measure of Angle A

An angle bisector is a line passing through the vertex of the angle that cuts the angle into two equal smaller angles.

Given: MN is angle bisector,

then  

           .......  [1]

Congruent angles are  two or more angles that have the same measure.

then;

by definition of congruent angles

[1]⇒                ......[2]

By the  Angle addition postulates states that if M is in the interior of ∠JMK then,

           ......[3]

Now, by substitution property ; substitute the equation [2] in [3] we get;

                ......[4]

Like terms terms whose variables  are the same

Combine like terms in equation [4] we get

                     ......[5]

Division property of equality states that you divide the same number to both sides of an equation.

Divide by 2 to both sides in equation [5] , we get