Question

(i) Prove with reason that if we produce one side of a triangle then the measurement of the exterior angle is sum of the measurement of two opposite interior angles.`​

Answer 1

refer the attachment hope its help u

Answer 2

Step-by-step explanation:

Exterior Angle Theorem

Statement: If a side of a triangle is produced, then the exterior angle so formed is equal to the sum of the two interior opposite angles.

Exterior angle theorem 2

Fig. 2 Exterior Angle Theorem

The above statement can be explained using the figure provided as:

According to the Exterior Angle property of a triangle theorem, the sum of measures of ∠ABC and ∠CAB would be equal to the exterior angle ∠ACD.

General proof of this theorem is explained below:

Proof:

Consider a ∆ABC as shown in fig. 2, such that the side BC of ∆ABC is extended. A line, parallel to the side AB