Question

find angle 3.
61
51
29

Explanation:

Step1: Find angle 1

The sum of angles in a triangle is \(180^{\circ}\).
\(\angle1 = 180^{\circ}-68^{\circ}-61^{\circ}=51^{\circ}\)

Step2: Use vertical angles

\(\angle1\) and \(\angle2\) are vertical angles, so \(\angle2=\angle1 = 51^{\circ}\)

Step3: Find angle 3

In the right - angled triangle with \(\angle2\), \(\angle3=180^{\circ}-90^{\circ}-\angle2\)
Substitute \(\angle2 = 51^{\circ}\), \(\angle3=180^{\circ}-90^{\circ}-51^{\circ}=39^{\circ}\)

Wait, there is a mistake above. Let's correct it.

Step1: Use vertical angles

The angle of \(61^{\circ}\) and the non - right angle adjacent to \(\angle2\) are vertical angles.
In the right - angled triangle where \(\angle3\) is located, we know that the sum of angles in a triangle is \(180^{\circ}\)
\(\angle3=180^{\circ}-90^{\circ}-61^{\circ}=29^{\circ}\)

Answer:

\(29^{\circ}\)