Observe Fig. 6.30 and then find P. Fig. 6.30
Step-by-Step Solution
Key Concept: Use the Exterior Angle Theorem: the exterior angle of a triangle is equal to the sum of the two interior opposite angles.
1. Identify the triangle in Fig. 6.30. Let the triangle be \(\triangle ABC\) with \(\angle A = 30^{\circ}\) and \(\angle C = 40^{\circ}\).\
2. The angle \(\angle P\) is the exterior angle at vertex \(B\) (i.e., the angle formed by extending side \(BC\) to point \(P\)).\
3. According to the Exterior Angle Theorem,\
$$\angle P = \angle A + \angle C.$$\
4. Substitute the known interior angles:\
$$\angle P = 30^{\circ} + 40^{\circ} = 70^{\circ}.$$\
5. Hence, the required angle \(\angle P\) measures \(70^{\circ}\).
Correct Answer: 70°