Question

Write a complete two-column proof for the following information. Hint: Use the Angle Addition Theorem and the fact that a line is made up of two opposite rays.



Given: m∠1 = 62° and lines t and l intersect

Prove: m∠4 = 62°

Answer 1

the answer goes like this

te konda hos ra eta bhobin hos
ae alu

Answer 2

Answer:

Given:

m∠1 = 62° and lines t and l intersect.

To Prove:

m∠4 = 62°.        

Solution:

Concept: “Two angles side by side with their vertices together creates a new angle whose measure equals the sum of the measures of the two original angles- Angle addition property”.

From the given figure,

m ∠1 + m∠ 2 = 180°                                (Straight line angles sums up 180)

On substitution, m∠1 = 62° gives;

       m∠ 2 = 180°-62°

                 = 118°

Similarly,

m∠ 2 + m∠4 = 180°   (Straight line angles sums up 180)

m∠4 = 180° - 118°

                    = 62°

Hence proved.