Geometry
posted by Kay .
A wooden plate is shaped as a pentagon. The measure of one angle is 20°. The remaining interior angles are obtuse and of equal measure.
What is the measure of each obtuse angle in the pentagon?

You know that a pentagon has 5 sides and 5 angles. So, if you already have one angle you only have to solve for four more, which happen to be equal. So, first determine the total degrees sum of the interior angles in a pentagon by using the formula: 180(n2) where n is the number of sides in the polygon. So, the sum of interior angles in a pentagon is 540. And now that you have one of them, you know the sum of the remaining 4 is 54020=520 degrees. And the problem also tells you that these last four angles are equal and obtuse! You are halfway done: just divided the remaining degrees, 520/4 and you get 130 degrees. Now check, is this obtuse? Yes, it is greater than 90 degrees but less than 180! Hope this helps!

140
Respond to this Question
Similar Questions

Geometry. Please help.
1) Two angles are complementary. The measure of one angle is 21 more than twice the measure of the other angle. Find the measure of the angles. 2) If a supplement of an angle has a measure 78 less than the measure of the angle, what … 
geometry
the measures of the interior angles of a pentagon are 2x, 6x, 4x6, 2x16 and 6x+2. What is the measure of the largest angle 
geometry
If an angle measures more than 90°, then it is an obtuse angle. What is the converse of this statement? 
geometry
obtuse triangle ABC with obtuse angle B. Point D on side AC such that angle BDC is also obtuse. Angle DAB is 2/3 of angle ABD. Angle BCD is 1/5 of angle CBD is 4 more than angle BAD. Find the measure of angle ABC. 
Geometry
Given: obtuse triangle ABC with obtuse angle B. Point D on side AC such that angle BDC is also obtuse. Angle DAB is 2/3 of angle ABD. Angle BCD is 1/5 angle BDC and angle CBD is 4 more than angle BAD. What is the measure of angle ABC? 
geometry
if the sum of the measure of four angles of a pentagon is 396, determine the measure of the fifth angle 
geometry
A picture frame is shaped as a heptagon. The measure of one angle is 126°. The remaining interior angles are congruent. What is the measure of each remaining interior angle in the picture frame? 
Geometry
If one of the interior angles of a pentagon has a measure of 48 degrees, what is the average measure of the pentagon's other interior angles ? 
math
An isosceles, obtuse triangle has one angle with a degree measure that is 50% larger than the measure of a right angle. What is the measure, in degrees, of one of the two smallest angles in the triangle? 
Geometry
I really need help with this question :( A pentagon has two exterior angles that measure (3x), two exterior angles that measure (2x + 22) and an exterior angle that measure (x + 41). If all of these angles have different vertices, …