Question

in the figure, ( mangle 1 = 39^circ ) and ( mangle 2 = 82^circ ). what is ( mangle 4 )? ( circ 98^circ ) ( circ 121^circ ) ( circ 133^circ ) ( circ 141^circ )

Explanation:

Step1: Find m∠3 using triangle angle sum

The sum of angles in a triangle is \(180^\circ\). So, \(m\angle 3 = 180^\circ - m\angle 1 - m\angle 2\). Substituting \(m\angle 1 = 39^\circ\) and \(m\angle 2 = 82^\circ\), we get \(m\angle 3 = 180^\circ - 39^\circ - 82^\circ = 59^\circ\).

Step2: Find m∠4 using linear pair

∠3 and ∠4 form a linear pair, so their sum is \(180^\circ\). Thus, \(m\angle 4 = 180^\circ - m\angle 3 = 180^\circ - 59^\circ = 121^\circ\).

Answer:

\(121^\circ\) (corresponding to the option with \(121^\circ\))