Question

13. In the figure, if AOB = 38" and BOC = 4x - 30°,
what value of x will make AOC a line?
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Answer 1

Answer:

x=30°

Step-by-step explanation:

AOC a line

<BOC+<BOA=180°(Linear pair)

4x-30°+3x=180°

7x-30°=180°

7x=180°+30°

7x=210°

x=210°/7

x=30°

Therefore, the value of x is 30°.

Answer 2

Given:-

• ∠AOB = 3x°

• ∠AOB = 4x - 30°

To find :-

• value of x which will make AOC a line.

Solution:-

Let's assume that AOC is a line

So, according to our assumption,

∠AOB + ∠AOB = 180°  (supplementary angles)

Substituting the values we have in the equation,

⤜ 3x + (4x - 30) = 180°

⤜ 3x + 4x - 30 = 180

⤜ 7x - 30 = 180

⤜ 7x = 180 + 30

⤜ 7x = 210

⤜ x = $\frac{210}{7}$

⤜ x = 30

∴ 30 is the value of x which will make AOC a line.

Verification:-

3x + (4x-30) = 180

3 × 30 + (4×30-30) = 180

90 + (120-30) = 180

90 + 90 = 180

Hence Proved