Question

find the value of x.
triangle with 35° angle at top, x° angle at bottom left, and 120° exterior angle at bottom right

Explanation:

Step1: Find the adjacent interior angle

The angle of \(120^\circ\) and its adjacent interior angle in the triangle are supplementary (they form a linear pair), so the adjacent interior angle is \(180^\circ - 120^\circ = 60^\circ\).

Step2: Use the triangle angle sum theorem

The sum of the interior angles of a triangle is \(180^\circ\). Let the angles of the triangle be \(35^\circ\), \(60^\circ\), and \(x^\circ\). Then we have the equation \(35^\circ + 60^\circ + x^\circ = 180^\circ\).
First, calculate the sum of the known angles: \(35^\circ+60^\circ = 95^\circ\).
Then, solve for \(x\): \(x^\circ=180^\circ - 95^\circ = 85^\circ\).

Answer:

\(x = 85\)