Question

Triangle MNP has vertices N(2, 2) and P(0, –2). The triangle is symmetric about the y-axis. What is the approximate measure of the largest angle in the triangle?

A.52.8°
B.60.0°
C.63.6°
D.82.9°

Answer 1

63.6

Explanation:

Triangle MNP has vertices N(2, 2) and P(0, –2). The triangle is symmetric about the y-axis. What is the approximate measure of the largest angle in the triangle?

A.52.8°

B.60.0°

C.63.6°

D.82.9°

Answer 2

Point M of the triangle is (-2,2) to make triangle MNP as shown in the attached image

Triangle MNP has a base of 4 units and a height of 4 units. We can work out the angle x and angle y using trigonometry ratio

We use tan ratio to find both angles


`Tan (x) = (opposite)/(adjacent)`

`Tan(x)= (4)/(2)`

`Tan(x)=2`

`Tan^(-1)(2)=63.43494882`

`Angle x=63.43`


`Tan(y)= (opposite)/(adjacent)`

`Tan(y)= (2)/(4)`

`Tan^(-1)(0.5)=26.56505118`

`Angle y=26.6`

Angle MNP = Angle NMP = 63.43 degrees (this is based on the fact that the triangle is an isosceles triangle)

Angle MPN = 2×26.6 = 53.2 degrees (we multiply by 2 as angle y is only a half of angle MPN - as shown in the diagram)