Question

Two opposite angles of a parallelogram are 3 x -2 degree and 50 degree - x .Find the number of degree in each angle???

Help me please....​

Answer 1

Correct question:

Two opposite angles of a parallelogram are

(3x-2) and (50-x)

Then find each angle of the parallelogram

Explanation:

Let us consider //gram ABCD

$\sf \angle A=(3x-2) \: and \: \angle C=(50-x)$

In a paralellogram ,

$\underline{\bf opposite\: angles \: are \: equal}$

$\bullet \angle A=\angle C$

$\bullet \angle B=\angle D$

Equating

$\longrightarrow \: \sf \: 3x - 2 = 50 - x$

$\longrightarrow \: \sf \: 3x + x = 50 + 2$

$\longrightarrow \: \sf \: 4x = 52$

$\longrightarrow \: \sf \: x = \dfrac{52}{4}$

$\longrightarrow \: \boxed{ \sf \: x = 13 \degree }$

Therefore

$\sf \angle A=\angle C=3(13)-2=37\degree$

we know that

$\boxed{\bf sum \: of \: adjacent\: angles =180\degree}$

$\sf \angle B=\angle D=180-37=143\degree$

Angles of the parallelogram are 37°,

143°,37°,143°

Answer 2

$\bold{\underline{\underline{\huge{\sf{AnsWer:}}}}}$

Measure of angle A = 37 °

Measure of angle B = 143°

Measure of angle C = 37°

Measure of angle D = 143°

$\bold{\underline{\underline{\huge{\sf{StEp\:by\:stEp\:explanation:}}}}}$

GiVeN :

• Two opposite angles of a parallelogram

1. (3x - 2)°
2. (50 - x)°

To FiNd :

• Measure of each angle of the parallelogram.

SoLuTiOn :

In ◼️ ABCD,

1. m $\bold{\angle{A}}$ = (3x - 2)°
2. m $\bold{\angle{C}}$ = (50- x)°

Property :

$\bold{\sf{\large{In\:a\:parallelogram\:opposite\:angles\:are\:congruent}}}$

$\longrightarrow$ $\bold{\sf{\angle{A\:=\:m{\angle{C}}}}}$

Block in the values,

$\longrightarrow$$\bold{\sf{3x-2\:=\:50-x}}$

$\longrightarrow$ $\bold{\sf{3x+x\:=\:50+2}}$

$\longrightarrow$ $\bold{\sf{4x=52}}$

$\longrightarrow$ $\bold{\sf{x\:=\:{\dfrac{52}{4}}}}$

$\longrightarrow$ $\bold{\sf{x=13}}$

Substitute x = 13 in the measures of angles.

•°• m$\bold{\angle{A}}$ = 3x - 2

m$\bold{\angle{A}}$ = 3(13) - 2

m $\bold{\angle{A}}$ = 39 - 2

m $\bold{\angle{A}}$ = 37°

m $\bold{\angle{A}}$ = m $\bold{\angle{C}}$

•°• m $\bold{\angle{C}}$ = 37°

Property :

$\bold{\sf{\large{Adjacent\:angles\:of\:parallelogram\:are\:supplementary}}}$

$\bold{\sf{Angle\:A\:+\:Angle\:B\:\:\:And\:\:Angle\:C\:+\:Angle\:D}}$$\bold{\sf{\underbrace{Pairs\:of\:adjacent\:angles\:of\:parallelogram}}}$

$\longrightarrow$$\bold{\sf{\angle{A\:+\:{\angle{B\:=\:180}}}}}$

Block in the values,

$\longrightarrow$ $\bold{\sf{37\:+\:B\:=\:180}}$

$\longrightarrow$ $\bold{\sf{B\:=\:180\:-37\:}}$

$\longrightarrow$ $\bold{\sf{B\:=\:143}}$

•°• Measure of angle B = 143°

$\longrightarrow$$\bold{\sf{C\:+\:D\:=\:180}}$

Block in the values,

$\longrightarrow$ $\bold{\sf{37\:+\:D\:=\:180}}$

$\longrightarrow$ $\bold{\sf{D\:=\:180\:-37\:}}$

$\longrightarrow$ $\bold{\sf{D\:=\:143}}$

•°• Measure of angle D = 143°