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 STEPSA. 5°B.15°C.75°D. 150°

Accepted Solution

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 equalBy 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 anglesthen, [tex]\angle WYX =2\angle XYZ[/tex] orSubstitute 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]