Question

in the following parallelogram find the measure of the angles marked as x,y,z

Answer 1

Step-by-step explanation:

y=65°,z=75°

I hope it helps you

Answer 2

Given

• ABCD is a Parallelogram.
• Opposite side's of parallelogram are 4x-3 and 3x+2 .
• ∠ABC = 70° , ∠BAC = y+10° and ∠ACD = 35°

To Find

• Value of x y and z.

Solution

We know that,

• Opposite sides of Parallelogram are Equal

$\therefore \small\sf{ AB = AC }$

$\\ \sf\implies 4x-3 = 3x+2$

$\sf\implies 4x - 3x =3 +2$

$\sf\implies x =5$

In Parallelogram ABCD.

• AB || DC and line AC is Transversal.

$\small{\sf \therefore \angle ACD = \angle BAC \: \: \: \: \: \: - - - by \: alternate \: interior \: angle }$

$\\ \implies \sf 35\degree = y +10$

$\implies \sf y = 35 - 10$

$\implies \sf y = 25$

$\sf\therefore \angle BAC = 25+10= 35\degree$

In ∆ ABC

• ∠ABC = 70° , ∠BAC = 35° and ∠ACD = z°.

${\therefore \sf \small ∠ABC + ∠BAC + ∠ACB = 180\degree \: \: \: \: \: - - - - \: angle \: sum \: property}$

${\sf 35 + 70 + z = 180\degree }$

${\sf 105 + z = 180\degree }$

${\sf z = 180\degree - 105 }$

${\sf z = 75 {}^{0} }$

$\: \: \: \: \: \: \: \underbrace{ \: \: \: \: \boxed{\text{ Hence, the value of x y and z is \bf{5 , 25 and 75} \sf{\normalsize{respectively}}}} \: \: \: \: }$