Question

please solve this question don't spam​

Answer 1

Answer :-

• ABCD is a parallelogram
• ∠A = 80°

and we know that,

• opposite angles of the parallelogram are equal.

and ∠A and ∠D are opposite angles

$\bold{: \implies \angle A = ∠ D } \\ \\ \bold{: \implies∠ D = 80 \degree }$

and , we know that

• sum of adjacent angles of the parallelogram is 180°

here, ∠D and ∠C are adjacent angles

$\bold{: \implies ∠D + ∠C = 180 \degree} \\ \\ \bold{: \implies 80 \degree + z = 180 \degree} \: \: \: \: \: \\ \\ \bold{: \implies z = 180 \degree - 80 \degree } \: \: \: \: \: \\ \\ \bold{: \implies \: \boxed{ \bold{z = 100 \degree }}} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

and ∠C and ∠B are opposite angles

$\bold{: \implies \: z = y} \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \bold{: \implies \: \boxed{ \bold{y = 100 \degree }}}$

here, ∠D and x are angles of linear pair

and we know that,

• sum of angles of the linear pair is 180°

$\bold{: \implies 80 \degree + x = 180 \degree } \\ \\ \bold{: \implies x = 180 \degree - 80 \degree } \\ \\ \bold{: \implies \boxed{ \bold{ x = 100 \degree}}} \: \: \: \: \: \: \: \: \: \: \:$

hence,

• x = 100°
• y = 100°
• z = 100°

Answer 2

$\begin{gathered} \bold{: \implies ∠D + ∠C = 180 \degree} \\ \\ \bold{: \implies 80 \degree + z = 180 \degree} \: \: \: \: \: \\ \\ \bold{: \implies z = 180 \degree - 80 \degree } \: \: \: \: \: \\ \\ \bold{: \implies \: \boxed{ \bold{z = 100 \degree }}} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \end{gathered}</p><p>and ∠C and ∠B are opposite angles</p><p>\begin{gathered} \bold{: \implies \: z = y} \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \bold{: \implies \: \boxed{ \bold{y = 100 \degree }}}\end{gathered}</p><p>here, \: ∠D \: and \: x \: are \: \\ angles \: of linear \: pair</p><p>and \: we \: know \: that, \: \\ </p><p>• </p><p> \: sum \: of \: angles \: of \: \\ \: \: the \\ \: linear \: pair \: \\ is \: 180° \\ </p><p>\begin{gathered} \bold{: \implies 80 \degree + x = 180 \degree } \\ \\ \bold{: \implies x = 180 \degree - 80 \degree } \\ \\ \bold{: \implies \boxed{ \bold{ x = 100 \degree}}} \: \: \: \: \: \: \: \: \: \: \: \end{gathered}$