Question 1-1
Which expression is equivalent to the measure of <4 in the image below?

Using the property of alternate angles , let's first make the pair of equal angles :

‎ㅤ‎ㅤ‎ㅤ➙ m∠1 = m∠ 5

‎ㅤ‎ㅤ‎ㅤ➙ m∠2 = m∠ 6

‎ㅤ‎ㅤ‎ㅤ➙ m∠4 = m∠3 + m∠ 5

‎ㅤ‎ㅤ‎ㅤ➙ Since , m∠ 5 = m∠1

‎ㅤ‎ㅤ‎ㅤ➙ m∠ 4 = m∠ 3 + m∠1

Alternate Angles :

Alternate angles are angles that occur on opposite sides of the transversal line and have the same size. Alternate angles are equal: We can often spot interior alternate angles by drawing a Z shape: There are two different types of alternate angles, alternate interior angles and alternate exterior angles.

example 2 – simplify: step 1: completely factor both the numerators and denominators of all fractions. step 2: change the division sign to a multiplication sign and flip (or reciprocate) the fraction after the division sign; essential you need to multiply by the reciprocal. step 3 : cancel or reduce the fractions.