Question

find the value of x.
68°
a. 138°
b. 78°
c. 68°
d. 56°

Explanation:

Step1: Identify triangle type

The triangle has two equal - side markings, so it is an isosceles triangle. In an isosceles triangle, the base - angles are equal.

Step2: Recall angle - sum property

The sum of the interior angles of a triangle is 180°. Let the two equal angles be \(x\) and the third angle be 68°. So, \(x + x+68^{\circ}=180^{\circ}\), which simplifies to \(2x+68^{\circ}=180^{\circ}\).

Step3: Solve for \(x\)

First, subtract 68° from both sides: \(2x=180^{\circ}-68^{\circ}=112^{\circ}\). Then divide both sides by 2: \(x = \frac{112^{\circ}}{2}=56^{\circ}\).

Answer:

d. 56°