Angles of a triangle: the sum and the exterior angle

Answer Key - Grade 8 Math Worksheet - Challenge Me

Circle the best answer, or write your answer on the line.

1. 1.

   Milo's roof is a triangle with angles x°, (3x)° and (2x + 30)°. How many degrees is the largest angle?

   80
2. 2.

   Noah's tent is a triangle with angles x°, (4x − 25)° and (5x + 35)°. How many degrees is the largest angle?

   120
3. 3.

   Pia's kite wing is a triangle with angles x°, (4x + 20)° and (5x)°. How many degrees is the largest angle?

   84
4. 4.

   Zee draws triangle UVW and extends side UV past corner V. Some of the angles use x. How many degrees is the outside angle at V?

   125
5. 5.

   Ari draws triangle YCD and extends side YC past corner C. Some of the angles use x. How many degrees is the outside angle at C?

   75
6. 6.

   Esme's tent frame is an isosceles triangle with a top angle of 46°. The bottom beam sticks out past one bottom corner. How many degrees is the outside angle at that corner?

   113
7. 7.

   Pia extends two sides of triangle UVW. The outside angle at U is 140° and at V is 119°. How many degrees is the inside angle at W?

   79
8. 8.

   Ren wants to show why the three angles of a triangle add to 180°. Ren places three copies of a scalene triangle side by side along a ruler. Why do the angles add to 180°?

   • Three copies fit corner to corner around a point, and a full turn is 360°, so they fill the circle
   • Three copies fit corner to corner along a straight line, and a straight line is 180°
   • The three sides are equal, so each angle is 60°, and 3 × 60 = 180, so scalene triangles work too
9. 9.

   Tala draws triangle CDF on paper and extends side CD past D. Why is the outside angle at D equal to angle C plus angle F?

   • The outside angle is the biggest angle in the picture, so it is the sum of the others
   • The outside angle and the inside angle at D make 360°, and the three inside angles make 180°
   • The outside angle and the inside angle at D make 180°, and the three inside angles also make 180°
10. 10.

    Luz extends one side at each corner of triangle CDF, going around the same way. The outside angles are 128°, 111° and 121°. What do the three outside angles add to?

    • 360°: a full turn
    • 180°: a straight line
    • 540°: three straight lines