Question

identifying an unknown value
what is the value of x?
160
70
40
140

Explanation:

Step1: Determine the type of triangle

The triangle has two equal - length sides (marked with the same tick marks), so it is an isosceles triangle. In an isosceles triangle, the base - angles are equal.

Step2: Use the angle - sum property of a triangle

The sum of the interior angles of a triangle is \(180^{\circ}\). Let the two equal angles be \(x\) (the base - angles). We know one angle is \(40^{\circ}\). So, \(x + x+40^{\circ}=180^{\circ}\).
This simplifies to \(2x=180^{\circ}- 40^{\circ}\).
\(2x = 140^{\circ}\).
Then \(x=\frac{140^{\circ}}{2}\).

Answer:

\(70\)