Question

17 label the diagram with the correct measures: drag & drop the answer note: use ctrl+d to drag the option via keyboard

Explanation:

Step1: Recall properties of isosceles triangle

In a triangle, if two sides are equal (marked by the red lines, so \(AC = BC\)), then the triangle is isosceles. In an isosceles triangle, the base - angles (\(\angle A\) and \(\angle B\)) are equal.

Step2: Use the angle - sum property of a triangle

The sum of interior angles of a triangle is \(180^{\circ}\). Let \(\angle A=\angle B = x\). We know \(\angle C = 70^{\circ}\). Then \(x + x+70^{\circ}=180^{\circ}\).
Simplify the equation: \(2x=180^{\circ}- 70^{\circ}=110^{\circ}\).
Solve for \(x\): \(x=\frac{110^{\circ}}{2}=55^{\circ}\)

Answer:

Both \(\angle A\) and \(\angle B\) are \(55^{\circ}\)