Question

In the given figure,lines XY and LM intersect at O. If ∠XOL = a, ∠LOP=b, ∠POY=90°, ∠XOM=c and a:b = 2:3, find the value of c.​

Answer 1

━━━━━━━━━━━━━━━━━━━━━━━━━

$\huge{\underline{\underline{\sf{\orange{</p><p>Question:-}}}}}$

In the given figure,lines XY and LM intersect at O. If ∠XOL = a, ∠LOP=b, ∠POY=90°, ∠XOM=c and a:b = 2:3, find the value of c.

━━━━━━━━━━━━━━━━━━━━━━━━━

$\huge{\underline{\underline{\sf{\orange{</p><p>Solution:-}}}}}$

It is given that a:b = 2:3.

So, let a=(2x)° and b=(3x°).

In the given figure OP stands on line XY.

∴ ∠XOP + ∠POY = 180°

⟹ ∠XOL + ∠LOP + 90° = 180°⠀⠀[∴ ∠POY=90°]

⟹ a + b + 90 = 180

⟹ a + b = 90

⟹ 2x + 3x =90 =5x=90=x =18.

$\therefore \: a = (2x)\degree = (2 \times 18\degree) = 36\degree \: and \: b = (3x)\degree = (3 \times 18)\degree = 54\degree.$

Again,ray OX stands ob line LM.

∠LOX + ∠XOM = 180°

⟹ a+c=180°

⟹ 36° + c =180° ⟹ c=(180°-36°)=144°

Hence,c=144°.

━━━━━━━━━━━━━━━━━━━━━━━━━

Answer 2

Answer:

In the given figure,lines XY and LM intersect at O. If ∠XOL = a, ∠LOP=b, ∠POY=90°, ∠XOM=c and a:b = 2:3, find the value of c.

━━━━━━━━━━━━━━━━━━━━━━━━━

\huge{\underline{\underline{\sf{\orange{ < /p > < p > Solution:-}}}}}

</p><p>Solution:−

It is given that a:b = 2:3.

So, let a=(2x)° and b=(3x°).

In the given figure OP stands on line XY.

∴ ∠XOP + ∠POY = 180°

⟹ ∠XOL + ∠LOP + 90° = 180°⠀⠀[∴ ∠POY=90°]

⟹ a + b + 90 = 180

⟹ a + b = 90

⟹ 2x + 3x =90 =5x=90=x =18.

\begin{gathered}\therefore \: a = (2x)\degree = (2 \times 18\degree) = 36\degree \: and \: b = (3x)\degree = (3 \times 18)\degree = 54\degree. \\ \end{gathered}

∴a=(2x)°=(2×18°)=36°andb=(3x)°=(3×18)°=54°.

Again,ray OX stands ob line LM.

∠LOX + ∠XOM = 180°

⟹ a+c=180°

⟹ 36° + c =180° ⟹ c=(180°-36°)=144°

Hence,c=144°.

Step-by-step explanation:

mark as brainlist answer