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Describing Triangles

Describing Triangles 1.18 - Solution

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a

A triangle always has an interior angle sum of 180.180^\circ. If we let x represent the unknown angle, we can write the following equation. 40+78+x=180 40^\circ+78^\circ+x=180^\circ Solve for x.

40+78+x=18040^\circ+78^\circ+x=180^\circ
118+x=180118^\circ+x=180^\circ
x=62x=62^\circ

The unknown angle has the measure 62.62^\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 90.90^\circ. If we let x represent the unknown angle, we can equate 180180^\circ with the sum of the measures of the angles in ABC.\triangle ABC. 90+50+x=180 90^\circ+50^\circ+x=180^\circ Solve for x.

90+50+x=18090^\circ+50^\circ+x=180^\circ
140+x=180140^\circ+x=180^\circ
x=40x=40^\circ

The measure of the unknown angle is 40.40^\circ.