Question

in the given figure ,angle AOC = [2x+15] and angle BOC = [3x - 45] . Find the values of angle AOC and angle BOC .​

Answer 1

Required Answer :-

We are given that , ∠AOC = 2x + 15 and ∠BOC = 3x - 45

From the given figure , ∠AOC and ∠BOC form linear pair.

➙ ∠AOC + ∠BOC = 180°

➙ 2x + 15 + 3x - 45 = 180°

➙ 5x + 15 - 45 = 180°

➙ 5x - 30 = 180°

➙ 5x = 180° + 30

➙ 5x = 210°

➙ x = 210/5

➙ x = 42

Now ,

• ∠AOC = 2x + 15 = 2(42) + 15 = 84 + 15 = 99°
• ∠BOC = 3x - 45 = 3(42) - 45 = 126 - 45 = 81°

Hence , The values of ∠AOC and ∠BOC are

$\huge{\boxed{\red{\sf{ {99}^{ \circ} \: and \: {81}^{ \circ} }}}}$

Note :-

Linear pair are a pair of adjacent angles formed by the intersection of two lines. Linear pair are always supplementary.

Answer 2

$\\ \\ \large\underline{ \underline{ \sf{ \red{given:} }}}$

• ∠AOC = 2x + 15

• ∠BOC = 3x - 45

$\\ \\ \large\underline{ \underline{ \sf{ \red{to \: find:} }}}$

• ∠AOC and ∠BOC.

$\\ \\ \large\underline{ \underline{ \sf{ \red{solution:} }}}$

∠ AOC and ∠ BOC make a linear pair.

And linear pair is equal to 180°

⇢ ∠AOC + ∠BOC = 180

⇢ 2x + 15 + 3x - 45 = 180

⇢ 5x - 30 = 180

⇢ 5x = 210

⇢ x = 42

▬▬▬▬▬▬▬▬▬▬▬▬

★ ∠AOC = 2x + 15

Putting x = 42...

↦ ∠AOC = 2(42) + 15

↦ ∠AOC = 84 + 15

↦ ∠AOC = 99°

______________________

★ ∠BOC = 3x - 45

Putting x = 42...

↦ ∠BOC = 3(42) - 45

↦ ∠BOC = 126 - 45

↦ ∠BOC = 81°

Hence , ∠AOC is 99° and ∠BOC is 81°.

▬▬▬▬▬▬▬▬▬▬▬▬▬ㅤㅤㅤㅤ

ㅤㅤㅤ

Verification :-

Sum of ∠AOC and ∠BOC should be 180°.

➯ 99 + 81 = 180

➯ 180 = 180 ㅤㅤㅤㅤㅤㅤ( verified )