Question

Consider the following parallelogram. Find the values of $x,y,z$ in each.

Answer 1

(i) using proportion of parallelogram

$x=\angle D+\angle B=60$

and $\angle A+\angle B=180$

$\angle A=180-60=120$

$[\angle A=\angle z={120}^o]$

and $[\angle z=\angle y=120]$

Hence $x={60}^o,=y={120}^o,z={120}^o$

(ii) From $I{I}^{gm}ABCD=\angle A=\angle C=y={120}^o$

now

$\angle A+\angle B=180$

$\angle B=60$

now $\angle B=x+\angle DBC={60}^o$

$x=60-35=25[\angle DBC={35}^o]$

$[x={25}^o]4[x=z={25}^o]$

Hence $[x=25=z]and[y={120}^o]$

(iii) In $△AOBx+{100}^o+\angle ABO={180}^o$

$x=180-100-\angle ABO$

$x=80-30=50[\angle ABO={30}^o]$

$[x={50}^o]$

and $[z={40}^o]$

In $△BOCy=180-80-40=60$

Hence $x={50}^o,y={60}^o,z={40}^o$

From $I{I}^{gm}ABCDz=\angle A=\angle C={70}^o$

and $\angle D+\angle C={180}^o$

$x+67+70={180}^o$

$x={180}^o-{137}^o={43}^o$

$[x={43}^o]$

now $y={180}^o-x$

$y=180-43={137}^o$

Hence $x={43}^o,y={137}^o$ & $z={70}^o$