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# Describing Triangles

## Describing Triangles 1.18 - Solution

a

A triangle always has an interior angle sum of $180^\circ.$ If we let x represent the unknown angle, we can write the following equation. $40^\circ+78^\circ+x=180^\circ$ Solve for x.

$40^\circ+78^\circ+x=180^\circ$
$118^\circ+x=180^\circ$
$x=62^\circ$

The unknown angle has the measure $62^\circ.$

b

It may look like that the two angles are unknown, but they are not. One of them is a right angle and it has the measure $90^\circ.$ If we let x represent the unknown angle, we can equate $180^\circ$ with the sum of the measures of the angles in $\triangle ABC.$ $90^\circ+50^\circ+x=180^\circ$ Solve for x.

$90^\circ+50^\circ+x=180^\circ$
$140^\circ+x=180^\circ$
$x=40^\circ$

The measure of the unknown angle is $40^\circ.$