Question

From the diagram below, Is m∠A = 105? and Is ∠B = 75?

Answer 1

$LINES \: \: AND \: \: ANGLES \\ \\ \\\\In \: the \: attached \: figure \: , \\ \\ Angles \: \: \: a \: \: \: and \: \: \: b \: \:, \: As \: shown \: above \: \\ are \: called \: Co - interior \: angles \\ \\ a \: + \: b \: = \: 180 \: ( \: True \: for \: all \: \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: Co - interior \: angles \: ) \\ \\ In \: the \: given \: question \: \: A \: \: and \: \: 105 \: \: \\ are \: Co - interior \: angles \\ \\ A \: \: + \: \: 105 \: \: = \: \: 180 \\ \: \: \: \: || \: \: A \: \: = \: \: 75 \: degrees \: \: \: || \: \: \: \: \: \: Ans. \\ \\ B \: \: and \: \: 75 \: \: are \: also \: \: Co - interior \: \\ angles\\ \\ B \: \: + \: \: 75 \: \: \: = \: \: 180 \\ \: \: \: \: || \: \: B \: \: = \: \: 105\: degrees \: \: || \: \: \: \: \: \: \: Ans.$

Answer 2

It is the other way around. Angle A = 75° and angle B = 105°.

105° and A are what they call allied/co-interior angles. They must add up to 180°. A= 180°-105° = 75°.

75° and B must also add up to 180°. 180°-75° = 105°.