pentagon has angles 145 deg, 74 deg; find meas. of other 3

[Sikendo]

1. A pentagon has two angles thatmeasure 145 degrees and 74 degrees. If the other angles are all congruent, what are thier measrements?

2. If a regular octagon has a perimeter of 200 centimeters, what is the measurement of each interior angle and each side?

3. A rhombus has one angle that measures 45 degrees. What are the measures of the remaining angles? If it's perimeter is 80 yards, what is the length of a side?

4. The sum of the measures of two adjacent sides and one diagonal in a rhombus equals 24 inches. When will the sum of the measures of the other sides and the other diagonal be 24 inches?

5. An isosceles triangle has a perimeter of 78 cm and one side measures 28 cm. How many different triangles could have a perimeter of 78 cm? Give the dimensions of each.

I just dont understand it...

 

[wjm11]

Re: I dont get it.

1. A pentagon has two angles thatmeasure 145 degrees and 74 degrees. If the other angles are all congruent, what are thier measrements?

A pentagon has five sides and five angles.

First figure out the sum of all the interior angles.

Next subtract (145 + 74) from the sum of all the interior angles.

That remainder is equally divided between the three remaining angles since they are congruent.

Hope that helps.

Please show us what your thoughts and work are on the remaining problems.

 

[Loren]

Being too lazy to memorize the formula for finding the measure of interior angles of a convex polygon, I found it useful to know that the sum of the exterior angles is 360°. So, if I wanted the sum of the interior angles, I would find the measure of one exterior angle of a regular polygon and subtract that from 180° to get the measure of one interior angle. Then if I wanted the sum of the interior angles, simply multiply the measure of one interior angle by the number of sides. You could do that, then subtract the measure of the two angles you have and divide the result by the number of remaining angles. There's one approach.