Since lines AB and GH are perpendicular, angle 20 measures 90° and the sum of the measures of angles 14 and 15 is 90°. Therefore, angle 14 = 15x + 6 – 90 and angle 15 = 18x – 90. Since the sum of angles 14 and 15 is 90°, (15x + 6 – 90) + (18x – 90) = 90, 33x – 174 = 90, 33x = 264, x = 8. Therefore, the sum of angles 20 and 14 is 15(8) + 6 = 126, and the measure of angle 14 is equal to: 126 – 90 = 36. Since angles 14 and 19 are vertical angles, angle 19 also measures 36°.

Angles 5, 12, 16, and 22 are alternating (vertical) angles; their measures are equal; 8x – 4 = 7x + 11, x – 4 = 11, x = 15; 8(15) – 4 = 120 – 4 = 116°. Notice that you could also substitute 15 into the measure of angle 22: 7(15) + 11 = 105 + 11 = 116°. The measure of angles 5, 12, 16, and 22 is 116°.

Angles 1 and 8 are both right angles. In addition to be equal, they are also supplementary, since 90 + 90 = 180°. Angles 19, 15, and 20 also add to 180°, since these angles form a line. Angle 1 + angle 8 = angle 19 + angle 15 + angle 20 = 180°

Angles 21, 17, and 11 are alternating angles; their measure are equal. Since angle 11 and angle 5 are supplementary (they combine to form a line), angles 21 and 5 must be supplementary. Therefore, x² + 11 = 180, x² = 169,(x + 13)(x – 13) = 0, and x = 13 (disregard the negative value of x, since every numbered angle is greater than 0). If x = 13, then the measure of angle 3 is 9(13) + 1 = 117 + 1 = 118°. Since angle 3 and angle 10 are vertical angles, angle 10 is also 118°.

Since lines EF and AB are perpendicular, angle 8 measures 90°. Therefore, 90 + angle 9 = 133°,133 – 90 = 43, so angle 9 measures 43°. Angles 3 and 9 form a line; the sum of their measures is 180°. The measure of angle 3 is equal to: 180 – 43 = 137°.