Question

The following figure shows a parallelogram $ABCD$.
Use the given informations to find the values of $x,y$ and $z$.

• A. $x=2,y={152}^{\circ }$ and $z={28}^{\circ }$
• B. $x=3,y={152}^{\circ }$ and $z={28}^{\circ }$
• C. $x=6,y={152}^{\circ }$ and $z={28}^{\circ }$
• D. $x=9,y={152}^{\circ }$ and $z={28}^{\circ }$

Answer 1

The correct option is B $x=3,y={152}^{\circ }$ and $z={28}^{\circ }$

Solving for x:-
Opposite sides of a parallelogram are equal. So we can equate both side to find x,
$2x+2=3x-1,or,2x-3x=-2-1\left(Takingxonsameside\right)or,-x=-3or,x=3x=3cmAnswer$
Solving for z:-
Sum of any two consecutive angles of a parallelogram is supplementary,i.e., 180
So we can write,
$\angle A+\angle B=180or,(z+50)+102=180or,z+152=180or,z=180-152or,z=28Answer$
Solving for y:-
ABCD is a paralleogram,
$\therefore AB\parallel CDandACisintersectinglines,so,\angle BAC=\angle ACD\left(Alternateanglesareequal\right)\angle ACD=28(As\angle BAC=28)Now,CDintersectsACSumofanglesformedbyintersectionoftwolineissupplementary.i.e.,\angle ACD+\angle y=180or,28+\angle y=180(As\angle ACD=28)or,\angle y=180-28or,\angle y=152Answer$