Question

find x,y,z
trapezium ​

Answer 1

Answer:

$\red \bigstar{ \frak{ \underline \purple{answer}}}$

Step-by-step explanation:

know some thing special

☆Sum of all the sides of a trpezium Is 360°

So, in the figure a trpezium's is of 360°

\_A+\_B+\_C+\_D=360°

=>X° +20°+y°+92°+2x°+10°=360°

=> x°+y°+x°+20°+92° +2°+10°=360°

=>2x°+y°+32°+92°=360°

=>2x°+y°+124°=360°

=>2x°+y°=360° -124°

=>2x°+y°=236°

=>x°+y°=236°/2°

=>x°+y°=118°

Also you could simplify

x+20+2x+10=180°

3x+30=180°

3x=180-30

3x=150

x=50

y+92=180

y=180-92

y=88

Answer 2

Given:

$\huge{\red{\texttt{A Trapezium ABCD}}}$

where,

$\implies \green{\mathtt{\angle A = x + 20\degree}}$

$\implies \green{\mathtt{\angle B = y}}$

$\implies \green{\mathtt{\angle C = 92\degree}}$

$\implies \green{\mathtt{\angle D = 2x + 10\degree}}$

$\texttt{\purple{Hence, Trapezium is a quadrilateral}}$

So, As we know,

$\boxed{\red{\texttt{The sum of adjacent angles of both}}} \\ \boxed{\red{\texttt{parallel sides is equal to 180°}}}$

So,

$\sf \green{\angle A + \angle D = 180 \degree} \\ \sf \green{Also, \: \angle B + \angle C = 180\degree}$

In,

$\: \sf \angle A \: \: and \: \: \angle D,$

$\therefore \: \sf 180\degree = x + 20 \degree + 2x + 10 \degree \\ \implies \sf 180 \degree = 3x + 30 \degree \\ \implies \sf 3x = 180 \degree - 30 \degree \\ \implies \sf 3x = 150 \degree \\ \sf \implies x = \frac{150\degree}{3} \\ \implies \sf \blue{x = 50 \degree}$

$\therefore \texttt{Value of \angle A } \\ \implies \sf \blue{x + 20\degree = 50\degree + 20\degree} \\ \implies \sf \red{70\degree}$

$\therefore \texttt{Value of \angle D } \\ \implies \sf \blue{2x + 10\degree = 2 \times 50\degree + 10\degree} \\ \implies \sf \blue{100\degree + 10\degree} \\ \implies \sf \red{110\degree}$

Similarly,

In $\: \sf \angle B \: \: and \: \: \angle C$

$\texttt{Value of \angle B }$

$\therefore \: \sf 180 \degree = y + 92\degree \\ \implies \sf y = 180\degree - 92 \degree \\ \implies \sf \blue{y = 88 \degree}$

Hence, we have

$\texttt{\blue{Value of \angle A = 70 \degree }} \\ \texttt{\blue{Value of \angle B = 88 \degree }} \\ \texttt{\blue{Value of \angle C = 92 \degree }} \\ \texttt{\blue{Value of \angle D = 110 \degree }}$

Also,

$\texttt{\red{Value of x = 50 \degree }} \\ \texttt{\red{Value of y = 88 \degree }}$