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# Mathematics Proove that the sum of interior angles of a trinagle is 180 degree.

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60 + 60 + 60.

Posted on Jan 28, 2008

• Cory Jan 28, 2008

And it's only spelt with one "o". (Prove)

• Cory Jan 28, 2008

Every corner of an equilateral triangle has an interior angle of 60deg and an exterior angle of 300deg (360-60).

For a right-angled triangle, obviously, the right-angle is 90deg. The other two interior angles are 45deg. Add them up - 180deg.

For an isosoles triangle, the two base angles are the same and the top angle must be 180-the base angles, and vice-versa.

For any triangle, the sum of the angles must be 180deg, or the lines will not converge.

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Posted on Jan 02, 2017

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## Related Questions:

### If M is the midpoint of triangle ABC, ACB = 30degrees and BMA = 45 degrees, calculate the size of BAC in degrees.

Since M is the mid point of the triangle, the distance of M from A,B and C is equal which means AM = BM = CM.
Therefore, MAB = MBA. In triangle MAB, MAB=45 degrees.
sum of angles in a triangle = 180 deg. So, sum of angles MAB and MBA = 180 - BMA = 180 -45 = 135.
Since both MAB and MBA are equal , MAB = 135/2 = 67.5
In triangle AMC, MAC = MCA . Therefore MAC = 30/2 = 15 deg.
Therefore total BAC = MAC + MAB =82.5 deg.

May 19, 2017 | Homework

### How many angles does a regular polygon have when its interior angle is 176 degrees

Lots and lots and lots. When you think the angle is nearly 180 degrees or a straight line, it must have lots and lots of sides.

The total of the interior angles of a polygon is given by (n-2)180, so the angle of each interior angle of a regular polygon is given by ((n-2)180)/n.

Now we set this to be equal to 176 and solve for n.
(n-2)180 = 176
-----------
n

Multiplying both sides by n, we get (n-2) 180 = 176n

Expanding the left side of the equation, 180n - 360 = 176n

Subtracting 176n from both sides and adding 360 to both sides, we get

180n - 176n = 360

4n = 360

Dividing both sides by 4, n = 90

Thus, you need a regular polygon of 90 sides to get an internal angle of 176 degrees.

Hopefully you don't have to construct it.

Good luck,

Paul

Mar 26, 2017 | Homework

### How many sides does a regular polygon have when the interior degrees is 176?

Lots and lots and lots. When you think the angle is nearly 180 degrees or a straight line, it must have lots and lots of sides.

The total of the interior angles of a polygon is given by (n-2)180, so the angle of each interior angle of a regular polygon is given by ((n-2)180)/n.

Now we set this to be equal to 176 and solve for n.
(n-2)180 = 176
-----------
n

Multiplying both sides by n, we get (n-2) 180 = 176n

Expanding the left side of the equation, 180n - 360 = 176n

Subtracting 176n from both sides and adding 360 to both sides, we get

180n - 176n = 360

4n = 360

Dividing both sides by 4, n = 90

Thus, you need a regular polygon of 90 sides to get an internal angle of 176 degrees.

Hopefully you don't have to construct it.

Good luck,

Paul

Mar 26, 2017 | Homework

### How to calculate angles

You need more information to be able to solve resolve the triangle.
All you can say is that the sum of the measures of the two unknown angles is
sum of values of the two angles =(180-76) degrees.

Nov 21, 2013 | Office Equipment & Supplies

### Their are three angle d first one is 128 degree, the second one is 37 degree, find x

I presume that x is the measure in degrees of the third angle. Use the fact the sum of the interior angle of a triangle is equal to 180 degrees.
x+128+37=180
x+165=180
x=180-165=15 degrees.

Sep 16, 2013 | Office Equipment & Supplies

### What is the sume of the measures of the interior angles of a hexagon

720 degrees; a triangle is 180, quadrilateral 360, pentagon, 540. Each angle a shape goes up ads 180 degrees.

Aug 25, 2011 | Texas Instruments TI-34II Explorer Plus...

### How do convex polygons differ from non-convex polygons?

A convex polygon is one with each of its interior angles less than 180 degrees and every line segment between any of its two vertices remains inside or on the boundary of the polygon.

Example of a convex polygon (WIKIPEDIA)

A concave polygon will always possess an interior angle with a measure that is greater than 180 degrees.

Example of a concave polygon (WIKIPEDIA)

Aug 11, 2011 | Computers & Internet

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