Question

a) in the figure, \\( \triangle abd \\) is an isosceles triangle with \\( ab = ad \\). find \\( m \angle \\)
b) if \\( \triangle ced \\) is an equilateral triangle, determine \\( m \angle aed \\)
3.2 check yo self
are you able to answer these questions on your own?

1. what is the value of \\( x \\) in the diagram?

\\( \

$$\begin{array} { l l l l } { \\text { a. } 49 ^ { \\circ } } & { \\text { b. } 59 ^ { \\circ } } & { \\text { c. } 54 ^ { \\circ } } & { \\text { d. } 90 ^ { \\circ } } \\end{array}$$

\\)

1. what is the value of \\( y \\) in the diagram?

\\( \

$$\begin{array} { l l l l } { \\text { a. } 49 ^ { \\circ } } & { \\text { b. } 59 ^ { \\circ } } & { \\text { c. } 54 ^ { \\circ } } & { \\text { d. } 90 ^ { \\circ } } \\end{array}$$

\\)

Explanation:

Step1: Find \(x\)

In a right - angled triangle, the sum of the two non - right angles is \(90^{\circ}\).
We know one non - right angle is \(36^{\circ}\), so \(x + 36^{\circ}=90^{\circ}\).
Subtracting \(36^{\circ}\) from both sides gives \(x = 90^{\circ}-36^{\circ}=54^{\circ}\).

Step2: Find \(y\)

In a right - angled triangle, the right angle is \(90^{\circ}\).
So \(y = 90^{\circ}\).

Answer:

1. C. \(54^{\circ}\)
2. D. \(90^{\circ}\)