Question

in parallelogram PQRS,angle P=x+10degree and angle Q=3x+20degree find the value of x​

Answer 1

$\huge \bold \color{green}{ \underline{ \underline \red{requied \: answer : }}}$

given :-

$\bold{pqrs \: is \: a \: parallelogram }\\ \bold{\angle p \: = x + 10} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \bold{\angle q = 3x + 20 }\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

since PQRS is a parallelogram so;

then,angle P and angle Q are adjacent angles

concept :-

sum of adjacent angles of a parallelogram is 180°

$\bold{ \implies \: \angle \: p + \angle \: q = 180 \degree} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \bold{\implies \:( x + 10 ) + (3x + 20) = 180} \\ \\ \bold{ \implies \: x + 10 + 3x + 20 = 180} \: \: \: \: \: \: \: \\ \\ \bold{ \implies \: 4x + 30 = 180} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \bold{ \implies \: 4x = 180 - 30 } \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \bold{ \implies \: x = \frac{150}{4} } \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \bold{ \implies x = 37.5 } \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

so value of x is 37.5

$\bold{ { \underline{ \underline {for \: more \: information : }}}}$

• sum of all angles of a parallelogram is 360°
• opposite angles of a parallelogram are equal
• opposite sides of a parallelogram are equal and parallel to each other
• diagonals of a parallelogram bisect each other
• sum of adjacent angles of a parallelogram is 180°

Answer 2

Answer:

$\huge \fbox \purple {answer}$

∠p=x+10

∠q=3x+20

since PQRS is a parallelogram so;

then,angle P and angle Q are adjacent angles

concept :-

sum of adjacent angles of a parallelogram is 180°

⟹∠p+∠q=180°

⟹(x+10)+(3x+20)=180

⟹x+10+3x+20=180

⟹4x+30=180

⟹4x=180−30

⟹x= 150/4

⟹x=37.5

so value of x is 37.5

• sum of all angles of a parallelogram is 360°
• opposite angles of a parallelogram are equal
• opposite sides of a parallelogram are equal and parallel to each other
• diagonals of a parallelogram bisect each other
• sum of adjacent angles of a parallelogram is 180°