Question

what are the values of b and c?
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Explanation:

Step1: Use the property of isosceles triangle

Since two sides of the triangle are equal (marked with the same tick - mark), the triangle is isosceles. In an isosceles triangle, the base - angles are equal. So, \(b = 61^{\circ}\).

Step2: Use the angle - sum property of a triangle

The sum of angles in a triangle is \(180^{\circ}\). Let the angles of the triangle be \(a = 61^{\circ}\), \(b = 61^{\circ}\), and \(c\). Then \(a + b + c=180^{\circ}\). Substitute \(a = 61^{\circ}\) and \(b = 61^{\circ}\) into the equation: \(61^{\circ}+61^{\circ}+c = 180^{\circ}\).

$$c=180^{\circ}-(61^{\circ}+61^{\circ})$$

$$c = 180^{\circ}-122^{\circ}$$

$$c = 58^{\circ}$$

Answer:

\(b = 61^{\circ}\), \(c = 58^{\circ}\)