Question

lesson 4 - 2: do now (day 2)
based on the isosceles triangle theorem, what is the value of x?
144°
51.5°
26°
77°

Explanation:

Step1: Recall the isosceles triangle theorem

In an isosceles triangle, the base - angles are equal. Let the two equal angles be \(x\) and \(77^{\circ}\). But wait, no, the sum of angles in a triangle is \(180^{\circ}\). Since the triangle is isosceles (marked by the equal - side indicators), and one of the non - equal angles is \(77^{\circ}\). Let's use the angle - sum formula for a triangle \(A + B + C=180^{\circ}\). Here, if the two equal angles are \(x\) and the third angle is \(77^{\circ}\), then \(x + x+77^{\circ}=180^{\circ}\).

Step2: Solve the equation

Combine like terms: \(2x=180^{\circ}-77^{\circ}\). So \(2x = 103^{\circ}\). Then \(x=\frac{103^{\circ}}{2}=51.5^{\circ}\).

Answer:

\(51.5^{\circ}\)