Question

Write a paragraph proof for the following conjecture:

Given: m∠1 +m∠2=m∠4
Prove: m∠3 +m∠1 +m∠2=180°

Answer 1

The answer to your question is given below.

Explanation:

From the question given,

m∠1 + m∠2 = m∠4

To prove that:

m∠3 + m∠1 + m∠2 = 180°

We simply do the following:

m∠3 + m∠4 = 180°.... (1) (angle on a straight line)

But from the question given,

m∠4 = m∠1 + m∠2

Substitute the value of m∠4 into equation (1)

m∠3 + m∠4 = 180°

m∠3 + m∠1 + m∠2 = 180° QED