Math: Parallelogram

Question

chuuuchaysTyro

Asked: April 13, 20212021-04-13T08:34:48+00:00 2021-04-13T08:34:48+00:00In: Geometry, High School/Senior Secondary School

If m∠𝑋𝑊𝑌 = (3x + 11)O and m∠𝑍𝑌𝑊 =
(7x – 1)O, when m∠𝑍𝑊𝑌 = (2y + 2)O and
m∠𝑋𝑌𝑊 = (3x – 2)O, then what is m∠𝑊 and m∠𝑌?

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acedstud · Answer 1 · 2021-04-14T09:11:23+00:00

acedstud

This answer was edited.

In a parallelogram, the alternate angles of the diagonals are equal.

Hence, $m\angle{XWY}\cong m\angle{ZYW}\Rightarrow(3x+11)^o=(7x-1)^o\Rightarrow3x+11=7x-1$ .

$\Rightarrow3x-7x=-1-11\Rightarrow-4x=-12\Rightarrow\dfrac{-4x}{-4}=\dfrac{-12}{-4}\Rightarrow x=3$ .

Also, $m\angle{ZWY}\cong m\angle{XYW}\Rightarrow(2y+2)^o=(3x-2)^o$ .

$\Rightarrow2y+2=3(3)-2=9-2=7=\Rightarrow2y=7-2=5\Rightarrow\dfrac{2y}{2}=\dfrac{5}{2}\Rightarrow y=2.5$ .

Therefore, $m\angle{W}=m\angle{XWY}+m\angle{ZWY}=(3x+11)^o+(2y+2)^o=(3(3)+11)^o+(2(2.5)+2)^o$

$=(9+11)^o+(5+2)^o=20^o+7^o=27^o$

Also, $m\angle{Y}=m\angle{ZYW}+m\angle{XYW}=(7x-1)^o+(3x-2)^o$

$=(7(3)-1)^o+(3(3)-2)^o=(21-1)^o+(9-2)^o=20^o+7^o=27^o$ .

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