Question

$\begin{gathered}{\Huge{\textsf{\textbf{\underline{\underline{\purple{Question:}}}}}}}\end{gathered}$
The measures of two adjacent angles of a parallelogram are in the ratio 4:5. Find the measure of each of the angles of the parallelogram.
⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀
● Don't Spam!!
● No Copied Answer
● Give Full Explanation
​

Answer 1

$\sf{\huge{\underline{\green{Given :-}}}}$

• The measures of two adjacent angles of a parallelogram are in the ratio 4:5.

$\sf{\huge{\underline{\green{To\:Find :-}}}}$

• The measure of each of the angles of the parallelogram.

$\sf{\huge{\underline{\green{Answer :-}}}}$

According to the question,

The measures of two adjacent angles of a parallelogram are in the ratio 4:5.

• ∠A = 4x

• ∠B = 5x

We know that opposite angles of parallelogram are equal

• ∠A = ∠C = 4x

• ∠B = ∠D = 5x

We know that, the sum of adjacent angles of a parallelogram is 180°.

∠A + ∠B = 180°

➝ 4x + 5x = 180°

➝ 9x = 180°

➝ x = 180°/9

➝ x = 20°

• ∠A = ∠C = 4x = 4 × 20° = 80°

• ∠B = ∠D = 5x = 5 × 20° = 100°

$\sf{\huge{\underline{\green{Verification :-}}}}$

We know that the parallelogram is a quadrilateral,

The sum of all angles around a quadrilateral .

∠A + ∠B + ∠C + ∠D = 360°

➝ 80° + 100° + 80° + 100° = 360°

➝ 180° + 180° = 360°

➝ 360° = 360°

______________________________________

Answer 2

$\boxed{\orange{\textsf{\textbf{ Here is the answer}}}}$

ㅤㅤㅤ

Let , ABCD be a parallelogram

Given ,

ㅤㅤRatios of the adjacent angles = 4:5

Let ,

ㅤㅤThe measure of the angle be x units

$\therefore$ L ABC = 4xㅤ&ㅤL BCD = 5x

ㅤㅤㅤ

∵ In a parallelogram

• Opposite sides are parallel ( || )
• Opposite angles are same

ㅤ

$\therefore$ L BAD = L BCD = 5x

ㅤㅤL ADC = L ABC = 4x

ㅤㅤㅤ

$\therefore$ L ABC + L BCD + L ADC + L BAD = 360⁰

ㅤㅤ➪ 4x + 5x + 4x + 5x = 360⁰

ㅤㅤ➪ 9x + 9xㅤ = 360⁰

ㅤㅤ➪ㅤ18xㅤ ㅤ= 360⁰

ㅤㅤ➪ ㅤxㅤㅤㅤ= $\sf{\dfrac{360}{18}}$

ㅤㅤ➪ ㅤxㅤㅤㅤ= $\sf{\dfrac{\cancel{360}^{180}}{\cancel{18}_{9}}}$

ㅤㅤ➪ ㅤxㅤㅤㅤ= $\sf{\dfrac{\cancel{180}^{60}}{\cancel{9}_{3}}}$

ㅤㅤ➪ ㅤxㅤㅤㅤ= $\sf{\dfrac{\cancel{60}^{20}}{\cancel{3}}}$

ㅤㅤ➪ㅤ xㅤㅤㅤ= $\sf{\bf{20}}$

ㅤㅤㅤ

• L ABC = L ADC = 4x

ㅤㅤㅤ ㅤㅤㅤㅤㅤㅤㅤ= 4 × 20

ㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤ = 80⁰

• L BCD = L BAD = 5x

ㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤ = 5 × 20

ㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤ = 100⁰

ㅤㅤㅤ

•°• L ABC + L BCD + L ADC + L BAD

ㅤ=ㅤ80⁰ + 100⁰ + 80⁰ + 100⁰

ㅤ=ㅤ180⁰ + 180⁰

ㅤ=ㅤ360⁰ㅤㅤㅤ. . . . = R.H.S

ㅤㅤㅤ

ㅤㅤㅤ꧁ ʙʀᴀɪɴʟʏ×ᴋɪᴋɪ ꧂