Assume a triangle ABC with a line AB (containing the side AB) with external angle D which is formed when line AB and line segment AC intersect. We are asked to prove that the external angle D is equal to the sum of the two interior angles B and C. Angles A and D are supplementary angles (they sum to 180 degrees) because they are linear angles (both together make a straight line, or a 180 degree angle). This means:
m<A + m<D = 180 degrees.
m<A = 180 deg - m<D
Then because A, B, and C are the three angles in a triange:
m<A + m<B + m<C = 180 deg
m<A = 180 deg - m<B - m<C
By substituting 180 deg - m<D in for m<A in the above equation we get:
180 deg - m<D = 180 deg - m<B - m<C
Subtract 180 deg from each side:
-m<D = -m<B - m<C
Multiply both sides by -1
m<D = m<B + m<C
Which proves that the measure of the external angle D is equal to the sum of the two opposite interior angles B and C for any given triangle.
wow. that's a lot. lol.
In a triangle, each exterior angle is equal to the sum of the two opposite interior angles.
The exterior angle of a triangle is equal to the sum of the two opposite interior angles. So if a triangle had points A, B and C: The exterior angle at B would equal the sum of interior angles at A and C. Similarly, the exterior angle at C would equal the sum of interior angles at A and B And the the exterior angle at A would equal the sum of interior angles at C and B.
No. It is equal to the sum of the opposite interior angles.
Any exterior angle of a triangle always equals the sum of the two interior opposite angles.
two opposite interior angles.
In a triangle, each exterior angle is equal to the sum of the two opposite interior angles.
The exterior angle of a triangle is equal to the sum of the two opposite interior angles. So if a triangle had points A, B and C: The exterior angle at B would equal the sum of interior angles at A and C. Similarly, the exterior angle at C would equal the sum of interior angles at A and B And the the exterior angle at A would equal the sum of interior angles at C and B.
No. It is equal to the sum of the opposite interior angles.
any other exterior angle of the triangle * * * * * No. The sum of the two opposite interior angles.
Any exterior angle of a triangle always equals the sum of the two interior opposite angles.
Interior Angles of a Triangle: 60 Exterior Angles of a Triangle: 120 Interior Angles of a Heptagon 128 (approx) Exterior Angles of A Heptagon 52 (approx) Answer: Triangle
two opposite interior angles.
Actually, no. The sum of the exterior angles of a triangle is 360 degrees. The sum of the interior angles of a triangle is 180 degrees.
an angle that forms a linear pair with one of the interior angles of the trinagle.(Apex)
The interior angles of a triangle add up to 180 degrees. The exterior angles of a triangle add up to 360 degrees.
The sum of the interior angles of any triangle is 180 degrees.
The exterior sum of the angles of any polygon including a triangle is always 360 degrees.