In the given figure,lines XY and LM intersect at O. If ∠XOL = a, ∠

1.	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» ━━━━━━━━━━━━━━━━━━━━━━━━━ $\huge{\underline{\underline{\sf{\orange{Question:-}}}}}$ 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. ━━━━━━━━━━━━━━━━━━━━━━━━━ $\huge{\underline{\underline{\sf{\orange{Solution:-}}}}}$ 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°. ━━━━━━━━━━━━━━━━━━━━━━━━━

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»

━━━━━━━━━━━━━━━━━━━━━━━━━

$\huge{\underline{\underline{\sf{\orange{Question:-}}}}}$

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.

━━━━━━━━━━━━━━━━━━━━━━━━━

$\huge{\underline{\underline{\sf{\orange{Solution:-}}}}}$

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°.

━━━━━━━━━━━━━━━━━━━━━━━━━