Question

Find the measure of angle 1

60 degrees
72 degrees
36 degrees
54 degrees

Answer 1

The sum of all angles (around the black dot) is 360°

All 5 angles (if you forget the red line) are the same; so each angle is 360°/5 = 72°

So Angle 1 is 72°

Answer 2

The required measure of angle 1 is 72°. Option B is correct.

In a figure pentagon is given with an angle mark at the center is 1, at vertex 3. The marked angle in the pentagon is to be determined.

What is the pentagon?

Pentagon is defined as a 5-sided polygon have equal lengths of sides and vertices making 72° at the center.

Number of sides in the pentagon = 5
Number of vertex on pentagon = 5
Angle made by vertices of the pentagon at the center = 360/5
                                                                                             = 72
Angle 1 = 72°
Now, Angle 2 = 1/2 of angle 1
                        =  1/2 * 72°
                        =  36°

Consider a right-angle triangle in the pentagon, containing angle 3.

The sum of the angle in a triangle is 180.
So, 90° + 36° +Angle 3 = 180
Angle 3 = 180 - 126
Angle 3 = 54°

Thus, the required measure of angle 1 is 72°.

Learn more about the pentagon here:

brainly.com/question/17054992

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