true or false

Question

a) Exterior angles of a triangle are never acute 

b) An exterior angle of a triangle may be equal to one of the interior angles

c) An exterior angle of a triangle may be smaller than one of the interior angles

d) all of the exterior angles of a triangle may be obtuse 

e) all of the exterior angles of a triangle may be acute

Answer 1

1) The sum of the exterior angles is 360°

 

2) An exterior angle is supplementary to its

adjacent interior angle

 

a) False, if the interior angle is obtuse, the exterior

    angle will be acute

 

b) if it were equal to one of the other interior

    angles, then that angle would be supplementary

    to the interior angle adjacent to the given exterior

    angle, giving you two interior angles adding up to 180°

   

    However, in a Right Triangle, the exterior angle adjacent

    to the right angle is also a right angle, therefore this is

    True

    

 

c) False, the exterior angle and the adjacent interior angle

    are supplementary, the adjacent interior angle added to 

    the other two interior angles makes 180° also, so the exterior

    angle is equal to the sum of the two remote interior angles

    (this is a geometric theorem: Exterior Angle Theorem)

 

d) True, equilateral triangle, all interior angles are 60°,

    all exterior angles are 120°

 

e) False, this would mean that all three interior angles were obtuse,

    adding them up would be greater than 180°

Answer 2

Two very important principals will help you answer all of these questions:

   1] the sum of the three interior angles of a triangle equals 180°.

   2] the sum of the three exterior angles of a triangle equals 180°.

 

Also, two definitions:

   1] an obtuse angle is greater than 90° but less than 180°

              (less than 180°.is required to form triangle)

   2] an acute angle is less than 90°.

 

a) Exterior angles of a triangle are never acute 

     The 20°-30°-160° triangle has an acute external angle of 20°.

b) An exterior angle of a triangle may be equal to one of the interior angles

     If a+b+c=180 then can (180-a)=c?     a+b+(180-a)=c    So, can b+180=c  ????

c) An exterior angle of a triangle may be smaller than one of the interior angles

         The 20°-30°-160° triangle has an external angle of 20°.

d) all of the exterior angles of a triangle may be obtuse

       If they are, a+b+c > 180

                       (>90) + (>90) + (>90) > 180

e) all of the exterior angles of a triangle may be acute

       If they are, a+b+c < 180
                       (<90) + (<90) + (<90) < 180