Question

angle sums of triangles
example two angles of a triangle measure 45° and 65°.
how many degrees must the third angle measure?
let ( x = ) measure of third angle.
( 45 ^ { circ } + 65 ^ { circ } + x = 180 ^ { circ } )
( 110 ^ { circ } + x = 180 ^ { circ } )
( 110 ^ { circ } - 110 ^ { circ } + x = 180 ^ { circ } - 110 ^ { circ } )
( x = 70 ^ { circ } )
the measure of the third angle is ( 70 ^ { circ } ).
directions calculate the measure of the missing angles.
1.
2.
3.
4.

Explanation:

Step1: Use the triangle angle - sum property

The sum of the interior angles of a triangle is \(180^{\circ}\). For each triangle, if two angles are known (\(a\) and \(b\)), then the third angle \(x\) can be found using the formula \(x = 180^{\circ}-(a + b)\)

Problem 1

• Given angles: \(90^{\circ}\) (right - angle) and \(20^{\circ}\)
• \(x=180^{\circ}-(90^{\circ}+20^{\circ})\)
• \(x = 180^{\circ}-110^{\circ}\)
• \(x = 70^{\circ}\)

Problem 2

• Given angles: \(55^{\circ}\) and \(40^{\circ}\)
• \(x=180^{\circ}-(55^{\circ}+40^{\circ})\)
• \(x = 180^{\circ}-95^{\circ}\)
• \(x = 85^{\circ}\)

Problem 3

• Given angles: \(35^{\circ}\) and \(80^{\circ}\)
• \(x=180^{\circ}-(35^{\circ}+80^{\circ})\)
• \(x = 180^{\circ}-115^{\circ}\)
• \(x = 65^{\circ}\)

Problem 4

• Given angles: \(110^{\circ}\) and \(40^{\circ}\)
• \(x=180^{\circ}-(110^{\circ}+40^{\circ})\)
• \(x = 180^{\circ}-150^{\circ}\)
• \(x = 30^{\circ}\)

Problem 5

• Given angles: \(90^{\circ}\) (right - angle) and \(70^{\circ}\)
• \(x=180^{\circ}-(90^{\circ}+70^{\circ})\)
• \(x = 180^{\circ}-160^{\circ}\)
• \(x = 20^{\circ}\)

Problem 6

• Given angles: \(90^{\circ}\) (right - angle) and \(67^{\circ}\)
• \(x=180^{\circ}-(90^{\circ}+67^{\circ})\)
• \(x = 180^{\circ}-157^{\circ}\)
• \(x = 23^{\circ}\)

Problem 7

• Given angles: \(92^{\circ}\) and \(47^{\circ}\)
• \(x=180^{\circ}-(92^{\circ}+47^{\circ})\)
• \(x = 180^{\circ}-139^{\circ}\)
• \(x = 41^{\circ}\)

Problem 8

• Given angles: \(64^{\circ}\) and \(53^{\circ}\)
• \(x=180^{\circ}-(64^{\circ}+53^{\circ})\)
• \(x = 180^{\circ}-117^{\circ}\)
• \(x = 63^{\circ}\)

Problem 9

• Given angles: \(24^{\circ}\) and \(127^{\circ}\)
• \(x=180^{\circ}-(24^{\circ}+127^{\circ})\)
• \(x = 180^{\circ}-151^{\circ}\)
• \(x = 29^{\circ}\)

Problem 10

• Given angles: \(90^{\circ}\) (right - angle) and \(38^{\circ}\)
• \(x=180^{\circ}-(90^{\circ}+38^{\circ})\)
• \(x = 180^{\circ}-128^{\circ}\)
• \(x = 52^{\circ}\)

Answer:

1. \(70^{\circ}\)
2. \(85^{\circ}\)
3. \(65^{\circ}\)
4. \(30^{\circ}\)
5. \(20^{\circ}\)
6. \(23^{\circ}\)
7. \(41^{\circ}\)
8. \(63^{\circ}\)
9. \(29^{\circ}\)
10. \(52^{\circ}\)