Answered

Discover a wealth of knowledge at Westonci.ca, where experts provide answers to your most pressing questions. Explore comprehensive solutions to your questions from a wide range of professionals on our user-friendly platform. Our platform provides a seamless experience for finding reliable answers from a network of experienced professionals.

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.

Thank you for choosing our platform. We're dedicated to providing the best answers for all your questions. Visit us again. Thank you for your visit. We're dedicated to helping you find the information you need, whenever you need it. Find reliable answers at Westonci.ca. Visit us again for the latest updates and expert advice.