Determine the measure of each angle: x, y and z
PLS HELP

x=42°

y=64°

z=68°

Step-by-step explanation:

Consider the triangle towards the right with 90° and 48° marked. The other angles must equal 42° (angles in a triangle add to 180, 42+48+90=180). This 42° angle is vertically opposite x, so x=42°.

The triangle that contains z also contains the angle 22° and 90° (because it is on a straight line with another 90° angle and the angles along a straight line add up to 180 (90+90=180)). Since the angles in a triangle add to 180, z=68°. (68+22+90=180)

The angles z, 48° and y lie along a straight line. Since the angles along a straight line equal 180 and since we know that z=68°, we can say y=64° (68+64+48=180)

Solve for x: (use triangle sum theorem)

48+90+x=180

x = 42 (vertical angles)

Solve for y: (Find z first, then use triangle sum theorem)

68+48+z=180

y = 64

Solve for z: (triangle sum theorem)

22+90+z=180

z=68

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