Question

angle relationships
brain dump
vocabulary
vocabulary
triangles
the sum of all the interior (inside) angles of a triangle is always equal to 180°
every exterior angle is supplementary to its adjacent interior angle
the measure of an exterior angle is equivalent to the sum of the remote interior angles.
remote interior angles do not share a vertex w/ the exterior angle

Explanation:

Step1: Use the exterior angle theorem

The exterior angle theorem states that an exterior angle of a triangle is equal to the sum of the two non - adjacent interior angles. In the given right - triangle, the right angle is \(90^{\circ}\), one of the non - adjacent interior angles is \(31^{\circ}\).

Step2: Calculate the value of \(x\)

We know that \(x = 90^{\circ}+31^{\circ}\) (by the exterior angle theorem).

$$x=90 + 31$$

$$x = 121$$

Answer:

\(121\)