Question

mark is making a decoration for a rally, using a string of triangular strips. each strip is an isosceles triangle when flattened out. what is the measure of the third angle? a 35° b 40° c 45° d 50° e 70°

Explanation:

Step1: Recall the property of triangle angles

The sum of the interior angles of a triangle is \(180^{\circ}\).

Step2: Use the property of isosceles triangle

In an isosceles triangle, two angles are equal. Let the equal angles be \(x\). Given one angle is \(40^{\circ}\).
Case 1: If \(40^{\circ}\) is one of the equal angles, then the third angle \(y = 180^{\circ}-40^{\circ}-40^{\circ}=100^{\circ}\) (not in the options).
Case 2: If \(40^{\circ}\) is not one of the equal angles, then the two equal angles \(x=\frac{180^{\circ}-40^{\circ}}{2} = 70^{\circ}\)

Answer:

E. \(70^{\circ}\)