Answer:
Option D is correct.
The measure of [tex]\angleWYX = 150^{\circ}[/tex]
Step-by-step explanation:
[tex]\triangle WXY[/tex] is isosceles and [tex]\angle YWX[/tex] and [tex]\angle YXW[/tex] are base angles.
Isosceles Triangle:
A triangle with two equal sides, and two congruent base angles that means the angles are equal
By the definition, the base angles are equal i.e, [tex]m\angle YWX=m\angle YXW[/tex]
Since, YZ bisects [tex]m\angle WYX[/tex]
Angle Bisector theorem: An angle bisector is a line or ray that divides an angle into two equal angles
then, [tex]\angle WYX =2\angle XYZ[/tex] or
Substitute the value of [tex]\angle XYZ=(15x)^{\circ}[/tex] ;
[tex]\angle WYX =2(15x)^{\circ} = (30x)^{\circ}[/tex]
The sum of measures of these three angles of triangle WXY is equal to the 180 degree.
In triangle WXY we have;
[tex]\angle YXW+\angle WYX+\angle YWX=180^{\circ}[/tex]
Substitute the value of [tex]m\angle YWX=m\angle YXW=(2x+5)^{\circ}[/tex] and [tex]\angle WYX=(30x)^{\circ}[/tex] in above formula:
[tex]2\angle YXW+30x=180^{\circ}[/tex] or
[tex]2\cdot(2x+5)+30x=180^{\circ}[/tex]
Simplify:
[tex]4x+10+30x=180^{\circ}[/tex]
Combine like terms ;
[tex]34x+10^{\circ}=180^{\circ}[/tex] or
[tex]34x=170^{\circ}[/tex]
Simplify;
[tex]x= \frac{170}{34} =5^{\circ}[/tex]
Substitute the value of x in [tex]\angle WYX [/tex];
[tex]\angleWYX = (30x)^{\circ} = 30 \cdot 5 = 150^{\circ}[/tex]
Therefore, the measure of [tex]\angleWYX = 150^{\circ}[/tex]
