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.