Question

exercise #3: for each isosceles triangle shown below, find the missing two angle measures.
(a)
(b)
(c)

Explanation:

(a)

Step1: Use the property of isosceles triangle

In an isosceles triangle \(ABC\) with \(AB = AC\), \(\angle B=\angle C\).

Step2: Use the angle - sum property of a triangle

The sum of angles in a triangle is \(180^{\circ}\). Let \(\angle B = \angle C=x\). We know \(\angle A = 66^{\circ}\). Then \(x + x+66^{\circ}=180^{\circ}\), \(2x=180^{\circ}- 66^{\circ}=114^{\circ}\), \(x = 57^{\circ}\).

(b)

Step1: Use the property of isosceles right - triangle

In right - triangle \(EFG\) with \(EG = FG\), \(\angle E=\angle F\).

Step2: Use the angle - sum property of a triangle

Since \(\angle G = 90^{\circ}\), and \(\angle E+\angle F+\angle G=180^{\circ}\). Let \(\angle E=\angle F = y\). Then \(y + y+90^{\circ}=180^{\circ}\), \(2y=90^{\circ}\), \(y = 45^{\circ}\).

(c)

Step1: Use the property of isosceles triangle

In isosceles triangle \(HIJ\) with \(HI = HJ\), \(\angle H=\angle J = 50^{\circ}\).

Step2: Use the angle - sum property of a triangle

Let \(\angle I=z\). Then \(z+50^{\circ}+50^{\circ}=180^{\circ}\), \(z=180^{\circ}-(50^{\circ}+50^{\circ})=80^{\circ}\).

Answer:

(a) \(\angle B = 57^{\circ}\), \(\angle C = 57^{\circ}\)
(b) \(\angle E = 45^{\circ}\), \(\angle F = 45^{\circ}\)
(c) \(\angle J = 50^{\circ}\), \(\angle I = 80^{\circ}\)