Question

In a given figure lines XY and MN intersects at O. If angle POY=90 and a:b=2:3, find C

Answer 1

Let a=2x
B=3x
2x+3x+90=180(linear pair)
5x. =90
X. =90/5=18
A=2×18=36
B=3×18=54
54+c=180(linear pair)
C. =180-54=126

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Answer 2

➢ Given :

• Lines XY and MN intersect at O.
• ${\angle}$POY = 90${\degree}$
• a : b = 2 : 3

➢ Solution :

✬ ${\angle}$POY = 90${\degree}$

✬ a : b = 2 : 3

• ${\angle}$XOY = 180${\degree}$(Straight line)
• ${\angle}$XOP + ${\angle}$POY = 180${\degree}$(Supplementary angle)
• ${\angle}$XOY + 90${\degree}$= 180${\degree}$(Given)
• ${\angle}$XOY = 180${\degree}$ - 90${\degree}$
• ${\angle}$XOP = 90${\degree}$

• ${\angle}$XOM + ${\angle}$MOP = ${\angle}$XOP (Complementary angle)
• 3x + 2x = 90${\degree}$
• 5x = 90${\degree}$
• x = ${\frac{90}{5}}$ = 18${\degree}$

✬ ${\angle}$MOP = 2x = 2 × 18 = 30${\degree}$

✬ ${\angle}$XOM = 3x = 3 × 18 = 54${\degree}$

• ${\angle}$MON = 180${\degree}$ (Straight angle)
• ${\angle}$MOX + ${\angle}$XON = 180${\degree}$ (Supplementary angle)
• 54${\degree}$+ ${\angle}$XON = 180${\degree}$
• ${\angle}$XON = 180${\degree}$ - 54${\degree}$
• ${\angle}$XON = 126${\degree}$

➢$\bold{\underline{\underline{Additional \ Information}}}$

$\bold{\underline{What \ is \ Straight \ angle : }}$

${\implies}$ Angle which measures 180${\degree}$

$\bold{\underline{What \ is \ Supplementary \ angle : }}$

${\implies}$ The 2 angles are Supplementary, If there sum are 180${\degree}$

$\bold{\underline{What \ is \ Complementary \ angle : }}$

${\implies}$ The 2 angles are complementary, If there sum are 90${\degree}$