Question

1. use the diagram to answer the question: what are the measures of the interior angles? 40°, 70°, 70° 70°, 70°, 70° 70°, 55°, 55° 70°, 10°, 10°

Explanation:

Step1: Find the measure of ∠ABC

Use the property of adjacent angles on a straight line.

$$ \angle ABC = 180^{\circ}- 110^{\circ}=70^{\circ} $$

Step2: Determine the type of triangle

Since \(AB = BC\), \(\triangle ABC\) is an isosceles triangle. So \(\angle BAC=\angle BCA\).

Step3: Calculate \(\angle BAC\) and \(\angle BCA\)

Use the angle - sum property of a triangle (\(\angle A+\angle B+\angle C = 180^{\circ}\)). Let \(\angle BAC=\angle BCA = x\).

$$ x + 70^{\circ}+x=180^{\circ} $$

$$ 2x=180^{\circ}-70^{\circ} $$

$$ 2x = 110^{\circ} $$

$$ x = 55^{\circ} $$

Answer:

\(70^{\circ},55^{\circ},55^{\circ}\)