Question

What is the value of x?

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x =

Two lines slightly inclined with horizontal intersect at the midpoint forming an obtuse angle. The above obtuse angle is labeled left square bracket 2 left parenthesis x plus 10 right parenthesis right square bracket degrees. The below obtuse angle is labeled left parenthesis 3 x minus 30 right parenthesis degrees.

Answer 1

The value of x is found to be 38 by setting the expressions for the two obtuse angles forming a straight line at their point of intersection equal to 180 degrees and solving for x.

Step-by-step explanation:

To find the value of x, we need to understand that the two lines intersect at a point creating an obtuse angle on both sides, implying that the sum of the two angles at the point of intersection is 180 degrees. Given the expressions for the angles, [2(x + 10)] degrees and (3x - 30) degrees, we set up the equation:

2(x + 10) + (3x - 30) = 180

Solving the equation step by step:

1. Distribute the 2 into the first parenthesis: 2x + 20.
2. Combine like terms: 2x + 20 + 3x - 30.
3. Simplify: 5x - 10 = 180.
4. Add 10 to both sides: 5x = 190.
5. Divide by 5: x = 190 / 5.
6. Simplify: x = 38.

Therefore, the value of x is 38.

Answer 2

Answer : The value of 'x' is,
`50^o`

Step-by-step explanation :

From the given figure we conclude that, the given angles are vertically opposite angles.

That means, the vertically opposite angles are equal.

`[2(x+10)]^o=(3x-30)^o`

Now rearranging the terms, we get:

`2x+20=3x-30`

`3x-2x=30+20`

`x=50^o`

Therefore, the value of 'x' is,
`50^o`