Question

I need this one done too please

Answer 1

a. ∠ 3 = 180° - ∠ 1 - ∠ 2

b. ∠ 4 = ∠ 1 + ∠ 2

c. 78°

Explanation:

a. If the measurements of two of the interior angles of a triangle are given, then the third angle can be measured as follows:

Let in Δ ABC, the ∠ 1 = ∠ A, ∠2 = ∠ B and ∠ 3 = ∠ C,

then if ∠ 1 and ∠ 2 are given then ∠ 3 = 180° - ∠ 1 - ∠ 2

This is because ∠ 1 + ∠ 2 + ∠ 3 = 180°.

b. Now, from the given diagram,

∠ 3 + ∠ 4 = 180° where ∠ 4 is the exterior angle

And ∠ 1 + ∠ 2 + ∠ 3 = 180°

Therefore, we can write ∠ 4 = ∠ 1 + ∠ 2 ........ (1)

c. If ∠ 4 = 120° and ∠ 2 = 42°

So, from equation (1), we have ∠ 1 = ∠ 4 - ∠ 2 = 120° - 42° = 78° (Answer)