Question

Triangle WXY is isosceles. ∠YWX and ∠YXW are the base angles. YZ bisects ∠WYX. m∠XYZ = (15x)°. m∠YXZ = (2x + 5)°. What is the measure of ∠WYX?
PLEASE EXPLAIN THE STEPS

A. 5°B.15°C.75°D. 150°

Answer 1

Answer:

Option D is correct.

The measure of $\angleWYX = 150^{\circ}$

Step-by-step explanation:

$\triangle WXY$ is isosceles  and $\angle YWX$ and $\angle YXW$ 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, $m\angle YWX=m\angle YXW$

Since, YZ bisects $m\angle WYX$

Angle Bisector theorem: An angle bisector is a line or ray that divides an angle into two equal angles

then, $\angle WYX =2\angle XYZ$ or

Substitute the value of $\angle XYZ=(15x)^{\circ}$ ;

$\angle WYX =2(15x)^{\circ} = (30x)^{\circ}$

The sum of measures of these three angles of  triangle WXY is equal to the 180 degree.

In triangle WXY we have;

$\angle YXW+\angle WYX+\angle YWX=180^{\circ}$

Substitute the value of $m\angle YWX=m\angle YXW=(2x+5)^{\circ}$ and $\angle WYX=(30x)^{\circ}$ in above formula:

$2\angle YXW+30x=180^{\circ}$ or

$2\cdot(2x+5)+30x=180^{\circ}$

Simplify:

$4x+10+30x=180^{\circ}$

Combine like terms ;

$34x+10^{\circ}=180^{\circ}$ or

$34x=170^{\circ}$

Simplify;

$x= \frac{170}{34} =5^{\circ}$

Substitute the value of x in  $\angle WYX$;

$\angleWYX = (30x)^{\circ} = 30 \cdot 5 = 150^{\circ}$

Therefore, the measure of $\angleWYX = 150^{\circ}$

Answer 2

Answer:

150 D

Step-by-step explanation: