Question

Note angles not necessarily drawn to scale

Answer 1

Answer:

x = 90° - 30° = 60°

Step-by-step explanation:

Angles CGE and 30° are vertical angles.

Thus, Angle CGE is thus 30°.

Angle CGE and Angle x are complementary, so x = 90° - 30° = 60°

Answer 2

The measure of angle EGB is 60 degrees.

What are vertically opposite angles?

Vertical Angles (Vertically Opposite Angles) When two lines intersect each other, then the opposite angles, formed due to intersection are called vertical angles or vertically opposite angles and they are always equal in measures.

What is right angle?

A right angle is an angle that is exactly equal to 90 degrees (or π/2) in measure.

According to the given question.

$m\angle FGD = 30^{o}$

Since, $\angle FGD$ and $\angle CGE$ are vertically opposite angles.

$\implies m\angle FGD = m\angle CGE = 30^{o}$

Now, $\angle CGB$ is a right angle.

Therefore,

$m\angle CGE + m\angle EGB = 90^{o}$

$\implies 30^{o} +x^{o} =90^{o}$

$\implies x^{o} =90^{o} -30^{o} \\\implies x^{o} = 60^{o}$

Hence, the measure of angle EGB is 60 degrees.

Find out more information about vertically opposite angles and right angle here:

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