MATH SOLVE

2 months ago

Q:
# LOTS OF POINTS MATH QUESTIONif the measure of the seven angles in a nonagon measure 138, 154, 145, 132, 128, 147, and 130 degrees. if the two remaining angles are equal in measure, what is the measure of each angle?

Accepted Solution

A:

In any polygon with number of sides = n, the sum of measures of its internal angles is equal to (n-2)*180

Now, for a nonagon:

number of sides = 9

sum of internal angles = (9-2)*180 = 1260 degrees

We are given the measures of seven of its angles and we know that the other two are equal. Assume that each angle of the remaining two angles has a measurements = x degrees

Therefore:

sum of angles = 138 +Β 154 + 145 + 132 + 128 + 147 + 130 + x + x

1260 = 974 + 2x

2x = 1260 - 974

2x = 286

x = 143 degrees

Based on the above calculations:

The measure of each angle of the remaining two angles is 143 degrees

Now, for a nonagon:

number of sides = 9

sum of internal angles = (9-2)*180 = 1260 degrees

We are given the measures of seven of its angles and we know that the other two are equal. Assume that each angle of the remaining two angles has a measurements = x degrees

Therefore:

sum of angles = 138 +Β 154 + 145 + 132 + 128 + 147 + 130 + x + x

1260 = 974 + 2x

2x = 1260 - 974

2x = 286

x = 143 degrees

Based on the above calculations:

The measure of each angle of the remaining two angles is 143 degrees