Question

. In the given figures, AOB is a straight line and the ray OC stands on Find the values of x and y
​

Answer 1

✍️ Question :-

In the figure, AOB is a straight line and ray OC stands on it. Find the value of x.

✍️ Answer :-

$\mapsto \sf <AOC + <BOC= 180°$ [Linear pair]

$\pink \mapsto \sf (5x-2)°+(2x+7)=180°$

$\mapsto \sf 5x-2+2x+7=180°$

$\pink \mapsto \sf 7x+5=180°$

$\mapsto \sf 7x=180°-5$

$\pink \mapsto \sf 7x=175$

$\mapsto \sf x= \Large \frac{175}{7}$

$\pink \mapsto \sf x =25$

Therefore, the value of x = 25°.

_________________________

Therefore, the angles are :-

• 5x-2 = 5(25°)-2 = 123°
• 2x+7 = 2(25°)+7 = 57°

Answer 2

Given

• AOB is a straight line
• OC stands on AOB
• ∠AOC = (5x-2)°
• ∠COB = (2x+7)°

To find

• Value of x
• Value of y

Solution

• ∠AOC + ∠BOC = 180°        (Linear Pair)
• (5x-2)° + (2x+7)° = 180°
• 5x - 2 + 2x + 7 = 180°
• 7x + 5 = 180°
• 7x = 180 - 5
• 7x = 175
• x = ¹⁷⁵⁄₇
• x = 25

☯ Value of x = 25°

• ∠AOC = (5x-2)°
• ∠AOC = (5(25)-2)°
• ∠AOC = 123°

☯  Value of ∠AOC = 123°

• ∠COB = (2x+7)°
• ∠COB = 2(25)+7)°
• ∠COB = 57°

☯ Value of ∠COB = 57°

Verification

• ∠AOC + ∠COB = 180°   (Linear Pair)
• 123° + 57° = 180°
• 180° = 180°