Question

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Given that A, O & B lie on a straight line segment, evaluate the size of the smallest angle.
C
A
(3a + 8)
0°
(60 - a)
O
(4a-38)
The diagram is not drawn to scale.
D
B

Answer 1

smallest angle = 35

Explanation:

the 3 angles lying on the straight line AOB sum to 180° , then

3a + 8 + 60 - a + 4a - 38 = 180 , that is

6a + 30 = 180 ( subtract 30 from both sides )

6a = 150 ( divide both sides by 6 )

a = 25

Then

3a + 8 = 3(25) + 8 = 75 + 8 = 83°

60 - a = 60 - 25 = 35°

4a - 38 = 4(25) - 38 = 100 - 38 = 62°

the smallest angle is 35°