PLS Help. Find the value of x in each of the following exercises:

The value of x is 120°

Explanation:

It is given that ABC is a straight line.

Also, ∠CBE = 20° and ∠CAF = 40°

We need to determine the value of ∠DBE

Let ∠DBE = x

Since, ∠CAF and ∠ABD are alternate interior angles.

By the alternate interior angles theorem, "if two parallel lines are cut by a transversal, then the pairs of alternate interior angles are equal".

Thus, ∠CAF and ∠ABD are equal.

Hence, ∠CAF = ∠ABD = 40°

Since, we know that, the angles in a straight line add up to 180°, we have,

∠ABD + ∠DBE + ∠CBE = 180°

Substituting the values, we get,

40° + x + 20° = 180°

Adding, we have,

60° + x = 180°

Subtracting both sides by 60, we have,

x = 120°

Thus, the value of x is 120°

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