Interior and exterior angle polygons. i need to find the measure of a regular decagon. to find each interior angle and to find each exterior angle

It may be easiest to remember that the sum of exterior angles of any convex polygon is always 360°.

Your decagon has a sum of exterior angles that is 360°. Since it is a regular 10-sided polygon, each one is 1/10 that value: 36°.

The measure of each exterior angle is 36°.

The measure of an interior angle is the supplement of the exterior angle. Each interior angle of the regular 10-sided polygon will be ...

... 180° -36° = 144°

The measure of each interior angle is 144°.

A formula often used for the sum of the measures of the interior angles is ...

... interior angle total = (n -2)×180°

For a 10-sided figure, the interior angle total is ...

... (10 -2)×180° = 1440°

When this sum is divided into 10 equal angles, the measure of one interior angle is ...

... 1440°/10 = 144° . . . . . agrees with the above computation

The exterior angle measure is the supplement of this:

... 180° -144° = 36° . . . . . exterior angle measure; agrees with the above computation

answer: option a.

step-by-step explanation:

you know that the quadrilateral opqr ( a four sided figure) is inscribed in circle. this means that all its vertices are on the circle.

then, by definition, the opposite angles of the quadrilateral are supplementary, this means that the sum of their measures is 180 degrees.

you can observe in the figure that the angles ∠opq   and the angle ∠orq   are opposite, therefore:

then, can be used to d to calculate the measure of ∠opq

x is greater than 5

step-by-step explanation:

2x+7 is greater than 17

    -7                           -7

2x is greater than 10

divide by 2 each side

x is greater than 5