Question

6. Find the value of x. 120 6x

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Answer 1

Applying the concept of the sum of angles on a straight line, we find that x equals 10°, demonstrating the practical application of mathematical principles in solving geometric problems.

To find the value of x, we can utilize the property that the sum of angles on a straight line is 180°. In this case, if one angle is 120°, then the other angle on the straight line is given by subtracting 120° from 180°, resulting in 60°.

Now, considering the angle opposite to the 120° angle, denoted as 6x, we can set up the equation 6x = 60°, as these angles are supplementary. Solving for x involves dividing both sides of the equation by 6, yielding x = 10°. Therefore, the value of x in this context is 10°.

This approach leverages the fundamental geometric concept of the sum of angles on a straight line to determine the unknown angle, showcasing how mathematical principles can be applied to solve problems related to angles and geometric figures.

Answer 2

Both angles are vertical angles. According to the Vertical Angles Theorem, vertical angles are congruent. Therefore:
6x°=120° [Vertical Angles Theorem (vertical angles are Congruent)].
6x/6=120/6 [Division P.O.E]
x=20.

Therefore, if x=20, then:
6(20)=120 [Substitution P.O.E.
120=120 [Symmetric P.O.E]

And thus,
x=20