Question

Angles E and F are vertical angles. If angle E has a measure of (4x+2)∘, and angle F has a measure of 70∘, what is the value of x?

17
22
45
70

Answer 1

Answer:

17 is the correct answer

Answer 2

Given:

Angles E and F are vertical angles.

If angle E has a measure of (4x+2)∘

angle F has a measure of 70∘

To find:

What is the value of x?

Solution:

From the Vertical Angle Theorem, we can say that

If two angles are vertical then they are equal to each other.

The measure of ∠E = (4x + 2)°

and

The measure of ∠F = 70°

Therefore, based on the above theorem, we get

$(4x + 2)\° = 70\°$

$\implies 4x = 70 - 2$

$\implies 4x = 68$

$\implies x = \frac{68}{4}$

$\implies \bold{x = 17}$

Thus, the value of x is → 17°.

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