Question

find the measure of the \?\ or \x\.
23°
? =

Explanation:

Step1: Recall the triangle angle - sum property

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

Step2: Use the property of an isosceles triangle

Since the two sides of the triangle are equal (marked with red lines), the triangle is isosceles. Let the vertex angle be \(23^{\circ}\), and the base angles be \(x\).
We know that in an isosceles triangle, the base angles are equal. So, \(x + x+23^{\circ}=180^{\circ}\).

Step3: Solve the equation for \(x\)

Combine like terms: \(2x+23^{\circ}=180^{\circ}\).
Subtract \(23^{\circ}\) from both sides: \(2x = 180^{\circ}- 23^{\circ}=157^{\circ}\).
Divide both sides by 2: \(x=\frac{157^{\circ}}{2}=78.5^{\circ}\).

Answer:

\(78.5^{\circ}\)