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# how to find the measurement of numbered angles

Question:I have a triangle. One angle is 88 degrees 40 minutes. The second angle is 37 degrees 52 minutes. Find the 3rd angle. I know the answer for this problem, however, I do not know how to solve it can anyone help me!!! The answer is 53 degrees 28 minutes.

Question:2.How do u find the measure of each interior angle of a polygon? 3. If I wanted to find the interior angle sum of a polygon with 102 sides would it be 1,800? Would the exterior angles be the same? 4. If I was given the number of sides on a polygon was 6, and I'm being asked to find the measure of each exterior and interior angle, would I use the same process? What would be the steps to solving the equation? Theorem 3.13 - The sum of the measure of the angles of a convex polygon with n sides is (n-2)180. Theorem 3.14- The sum of the exterior angles of any convex polygon, one angle at each vertex, is 360. (What is the vertex? Is that were two or more lines of the polygon meet?) Please help me.

Answers:[06] 1.If it is a regular polygon,a polygon having all sides equal,then you can get it directly by dividing 360 degrees by the no of sides. Otherwise,if you know the measure of interior angle/s,you may obtain the exterior angle by subtracting the measure of interior angle from 180 degrees 2.As you know,the sum of measure of interior angles of a polygon is given by the formula(n-2)*180.Hence if the polygon is a refular one we can find the measure of the interior angle by dividing the sum of measures of the angles by n In other words Interior angle of a regular polygon =(n-2)*180/n 3.It is (102-2)*180=18000 degrees 4.You may follow the same process but it is easier to find out the exterior angles first and then to obtain the interior angle by subtracting exterior angle from 180 degrees.In that case ,lot of calculation time will be saved Let us consider the case of a 6-sided regular polygon As we know the sum of exterior angles is always 360 degree Therefore measure of each exterior angle =360/6=60 degrees Interior angle=180-60=120 degrees 5)Do you want me to explain how this therem can be proved? 6)Theorem3.14- Vertex literally means the topmost point.In geometry,in the cases of all polygons ,the point at which two sides meet is called a vertex.Hence in a triangle ABC,there are three vertices A,B and C. Similarly a quadrilater ABCD has 4 vertices,A,B,C and D.

Question:So I have a triangle with one 90 degree angle, and I have to find the measurement of one of the other angles. The length of the side opposite the 90 degree angle is 23 units, and the length of the side on th left that goes vertically up and is part of the 90 degree angle is 12 units. How would I find the measure of the angle on the bottom horizontal part of the triangle thats all the way to the right, opposite of the 90 degree angle all the way to the left?

Answers:Let x = measure of angle. Since angle is opposite side of length 12, then sin(x) = 12/23 (opposite/hypotenuse) x = arcsin(12/23) Using a calculator to find x in degrees (using inverse sine function), we get: 31.44898

Question:ok this is the problem: http://i712.photobucket.com/albums/ww122/surfinthegreenmachine/lined_paper.gif i got measure of angle 1 and angle 3 is 135 measure of angle 2 and angle 4 is 45 ...because they're adjacent angles which means they're congruent..? i don't know if i'm doing this right..i was absent the day we learned this so yeah.. please explain how you found the answer and show your work .. thanks :)

Answers:Given: angle 4 = 3x + 15 angle 2 = 2x + 25 since both angles are adjacent angles, they are equal. so 3x + 15 = 2x + 25 Now get x: 3x - 2x = 25 - 15 x = 10 Now fill in this x in one of the equations: angle 4 = 3x + 15 = 3*10 + 15 = 30 + 15 = 45 Since angle 4 = angle 2: angle 2 = 45 Since the sum of all 4 angles must be 360 and angle 1 = angle 3: 360 = 45 + 45 + a + a 360 - 2*45 = 2*a (360 - 90) / 2 = a a = 135 So angle 1 = angle 3 = 135 Conclusion: Angle 1 = 135 Angle 2 = 45 Angle 3 = 135 Angle 4 = 45