Question

The measures of the angles of a quadrilateral are 49,58 and 127 what is the measure of the fourth angle

Answer 1

Tip:

Recall the total measurement of interior angles of a polygon.

Sum of interior angles $=(n-2)\times180$, where $n$ is the number of sides

Given:

Angles of a quadrilateral: $49^\circ,58^\circ,127^\circ$

Explanation:

Since the polygon is a quadrilateral, the polygon has $4$ sides

Sum of interior angles $=(n-2)\times180$

$\implies (4-2)\times180$

$\implies 2\times180$

$\implies 360^\circ$

The sum of the given angles,

$\implies 49+58+127$

$\implies 234^\circ$

The measure of the fourth angle

$\implies 360-234$

$\implies 126^\circ$

The measurement of the fourth angle is $126^\circ$