Question

Given the measure of three angles in a quadrilateral, find the measure of the fourth angle.1. 40 degree , 120 degree , 100 degree , _____2. 73 degree, 107 degree, 122 degree

Answer 1

Recall that the interior angles of a quadrilateral add up to 360 degrees.

1) Let x be the measure of the missing angle, then we can set the following equation:

$40^{\circ}+120^{\circ}+100^{\circ}+x=360^{\circ}.$

Solving for x we get:

$\begin{gathered} 260^{\circ}+x=360^{\circ}, \\ x=100^{\circ}\text{.} \end{gathered}$

2) Let y be the measure of the missing angle, then we can set the following equation:

$73^{\circ}+107^{\circ}+122^{\circ}+y=360^{\circ}\text{.}$

Solving for y we get:

$\begin{gathered} 302^{\circ}+y=360^{\circ}, \\ y=58^{\circ}\text{.} \end{gathered}$

Answer:

1) 100 degrees.

2) 58 degrees.