
(a)
To calculate: the measure of ∠XWZ .
(a)

Answer to Problem 1CYP
∠XWZ=45
Explanation of Solution
Given: WXYZ is an isosceles trapezoid and m∠YZW=45 , WV=15cm and VY=10cm
Formula Used:
Isosceles trapezoid is a convex quadrilateral with a line of symmetry bisecting one pair of opposite sides.
Calculation:
Consider an isosceles trapezoid WXYZ as follows:
Since WXYZ is an isosceles trapezoid,
Thus, △XWZ≅△YZW
Therefore, ∠XWZ=∠YZW (since corresponding
∠XWZ=45
Conclusion:
Hence, ∠XWZ=45
(b)
To calculate: the measure of ∠WXY .
(b)

Answer to Problem 1CYP
∠WXY=135
Explanation of Solution
Given: WXYZ is an isosceles trapezoid and m∠YZW=45 , WV=15cm and VY=10cm
Formula Used:
Isosceles trapezoid is a convex quadrilateral with a line of symmetry bisecting one pair of opposite sides
Calculation:
Consider an isosceles trapezoid WXYZ as follows:
Since WXYZ is an isosceles trapezoid,
Thus, XY is parallel to WZ
Therefore, ∠XWZ=∠YZW (consecutive interior angles are supplementary)
∠XWZ+∠WXY=18045+∠WXY=180∠WXY=180−45∠WXY=135
Conclusion:
Hence, ∠WXY=135°
(c)
To calculate: the measure of XZ .
(c)

Answer to Problem 1CYP
XZ=25cm
Explanation of Solution
Given: WXYZ is an isosceles trapezoid and m∠YWZ=45 , WV=15cm and VY=10cm
Formula Used:
Isosceles trapezoid is a convex quadrilateral with a line of symmetry bisecting one pair of opposite sides
Calculation:
Consider an isosceles trapezoid WXYZ as follows:
Since WXYZ is an isosceles trapezoid,
Thus, △XWZ≅△YZW
Therefore, XZ=YW (since corresponding sides of congruent triangles are equal)
XZ=WV+VYXZ=15+10XZ=25cm
Conclusion:
Hence, XZ=25cm .
(d)
To calculate: the measure of XV .
(d)

Answer to Problem 1CYP
XV=10cm
Explanation of Solution
Given: WXYZ is an isosceles trapezoid and m∠YWZ=45 , WV=15cm and VY=10cm
Formula Used:
Isosceles trapezoid is a convex quadrilateral with a line of symmetry bisecting one pair of opposite sides
Calculation:
Consider an isosceles trapezoid WXYZ as follows:
Since WXYZ is an isosceles trapezoid,
Thus, △XZY≅△YWX
Therefore, ∠ZXY=∠WYX (since corresponding angles of congruent triangles are equal)
Now, consider triangle XYV
Since ∠ZXY=∠WYX
Thus, XV=YV (sides opposite to equal angles are equal)
Hence, XV=10cm
Conclusion:
Hence, XV=10cm
Chapter 6 Solutions
Geometry, Student Edition
Additional Math Textbook Solutions
Calculus: Early Transcendentals (2nd Edition)
Elementary Statistics (13th Edition)
Basic Business Statistics, Student Value Edition
Introductory Statistics
A First Course in Probability (10th Edition)
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