Question

In a parallelogram ABCD, if ∠A = (3x + 12)˚, ∠B = (2x – 32)˚. Find x,

m∠ C, m∠D​

Answer 1

..Question.. ㅤ

In a parallelogram ABCD

if ∠A = (3x + 12)˚

∠B = (2x – 32)˚.

Find x and ∠ C and ∠D

..Answer..

Given here ,

ㅤㅤㅤㅤㅤㅤ➪ ∠ A = ( 3x + 12 )⁰

ㅤㅤㅤㅤㅤㅤ➪ ∠ B = ( 2x - 32 )⁰

☯︎ We are to find ' x '

°•° We know that ,

ㅤㅤ➪ ∠ A + ∠ B = 180⁰

[ sum of adjacent angles is 180⁰ ]

ㅤㅤ➪ ( 3x + 12 )⁰ + ( 2x - 32 )⁰ = 180⁰

ㅤㅤ➪ 3x + 12 + 2x - 32 = 180

ㅤㅤ➪ 3x + 2x + 12 - 32 = 180

ㅤㅤ➪ 5x - 20 = 180

ㅤㅤ➪ 5x = 180 + 20

ㅤㅤ➪ x = 200/5

ㅤㅤ➪ x = 40

•°• ∠ A = ( 3x + 12 )⁰

ㅤ ㅤ ㅤ= ( 3 × 40 + 12 )⁰

ㅤㅤㅤ = ( 120 + 12 )⁰

ㅤㅤㅤ = 132⁰

ㅤ ∠ B = ( 2x - 32 )⁰

ㅤㅤ ㅤ= ( 2 × 40 - 32 )⁰

ㅤㅤㅤ = ( 80 - 32 )⁰

ㅤㅤㅤ = 48⁰

Also we have to find , ∠ C and ∠ D

°•° In a parallelogram , opposite sides and angles are equal.

•°• ∠ A = ∠ C

ㅤㅤㅤ➪ 132⁰ = ∠ C

ㅤㅤㅤ➪ ∠C = 132⁰

also ,

ㅤㅤㅤ➪ ∠ B = ∠ D

ㅤㅤㅤ➪ 48⁰ = ∠ D

ㅤㅤㅤ➪ ∠ D = 48⁰

____________________

Give a look here ,

• angle sum property of triangle = 180⁰
• angle sum property of quadrilateral = 360⁰
• sum of 2 adjacent angles = 180⁰
• Linear pair = 180⁰

ㅤㅤㅤㅤ ꧁ ʙʀᴀɪɴʟʏ×ᴋɪᴋɪ ꧂

ㅤ