Answered

Westonci.ca is the premier destination for reliable answers to your questions, provided by a community of experts. Discover in-depth answers to your questions from a wide network of professionals on our user-friendly Q&A platform. Connect with a community of professionals ready to help you find accurate solutions to your questions quickly and efficiently.

In the diagram below of triangle UVW, X is a midpoint of UV and Y is a
midpoint of VW. If mZXYV = 7x + 21, and mZUWY = 91 – 7x,
what is the measure of ZXY?
V
X
Y
U
W

In The Diagram Below Of Triangle UVW X Is A Midpoint Of UV And Y Is A Midpoint Of VW If MZXYV 7x 21 And MZUWY 91 7x What Is The Measure Of ZXY V X Y U W class=

Sagot :

Given:

In triangle UVW, X is the midpoint of UV and Y is the midpoint of VW.

[tex]m\angle XYV=7x+21[/tex]

[tex]m\angle UWY=91-7x[/tex]

To find:

The measure of angle XYV.

Solution:

Since X is the midpoint of UV and Y is the midpoint of VW, therefore XY is the mid-segment of the triangle UVW and parallel to the base of the triangle, i.e., UW.

If a transversal line intersect two parallel lines, then the corresponding angles are congruent and their measures are equal.

[tex]\angle XYV \cong \angle UWY[/tex]         [Corresponding angle]

[tex]m\angle XYV=m\angle UWY[/tex]

[tex]7x+21=91-7x[/tex]

We need to solve this equation for x.

[tex]7x+7x=91-21[/tex]

[tex]14x=70[/tex]

[tex]x=\dfrac{70}{14}[/tex]

[tex]x=5[/tex]

Now,

[tex]m\angle XYV=7x+21[/tex]

[tex]m\angle XYV=7(5)+21[/tex]

[tex]m\angle XYV=35+21[/tex]

[tex]m\angle XYV=56[/tex]

Therefore, the measure of angle XYV is 56 degrees.

We appreciate your time on our site. Don't hesitate to return whenever you have more questions or need further clarification. Thank you for your visit. We're dedicated to helping you find the information you need, whenever you need it. Keep exploring Westonci.ca for more insightful answers to your questions. We're here to help.