geometry

posted by .

how can we prove that an exterior angle of a triangle has measure equal to the sum of the measures of the 2 interior angles remote from it

  • geometry -

    in triangle ABC extend BC to form the exterior angle at C, call that x

    We know angle A + Angle B + angle C = 180
    But angle C + x = 180, (by supplementary angle theorem)

    so angle A + angle B + angle C = x + angle C
    subtract angle C from both sides

    angle A + angle B = x, the exterior angle

    Therefore, the exterior angle of a triangle has measure equal to the sum of the measures of the 2 interior angles remote from it

  • geometry -

    rocks 12

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. Geometry

    What is the sum of the measures of the interior angles of a convex octagon?
  2. Geometry

    The measure of an exterior angle of a triangle is 120. the interior angles that are not adjacent to this exterior angle are congruent. find the measures of the interior angles of the triangle
  3. Geometry

    If the measure of an exterior angle of a triangle is 75 degrees, then what are the measures of the two remote interior angles?
  4. geometry

    The sum of the measures of two exterior angles of a triangle is 264o. What is the measure of the third exterior angle?
  5. math

    Find the measure of the interior angle in a regular polygon if the ratio of the sum of the measures of the interior angles to the sum of the measures of the exterior angels is 4
  6. GEOMETRY

    The sum of the measures of two exterior angles of a triangle is 264o. What is the measure of the third exterior angle?
  7. math

    One interior angle of a triangle has a measure that is equal to the sum of the measures of the other two angles of the triangle. What is the measure of the smallest exterior angle of the triangle in degrees?
  8. Geometry

    A right triangle has exterior angles at each of its acute angles with measures in the ratio 13:14. Find the measure of the smallest interior angle of the triangle. 40 (degrees) 50 (degrees) 130 (degrees) 140 (degrees) Please help?
  9. Math

    the measure of an exterior angle of a trangle is 125 the measure of one of its remote interiot angles is 65 what is the measure of the other remote interior angle
  10. Math

    Prove that an exterior angle of a triangle is equal to the sum of the non adjacent interior angles of that triangle. Use the following variables in your proof. Exterior angle=w Interior adjacent angle= x Interior non adjacent angle1= …

More Similar Questions