Question

(the figure is not to scale.)

Explanation:

Step1: Find the third angle of the triangle

The sum of the interior angles of a triangle is \(180^\circ\). Let the third angle be \(x\). So, \(x + 62^\circ+ 57^\circ= 180^\circ\). Solving for \(x\), we get \(x = 180^\circ-(62^\circ + 57^\circ)=180^\circ - 119^\circ = 61^\circ\).

Step2: Use the exterior angle theorem

The exterior angle (angle 1) is equal to the sum of the two non - adjacent interior angles. So, angle 1 \(= 62^\circ+ 57^\circ\) (or we can also use the fact that angle 1 and the third angle we found are supplementary, but using the exterior angle theorem is more direct here). Calculating \(62^\circ+ 57^\circ = 119^\circ\).

Answer:

\(119^\circ\)