Question

If the measure of angle 3 is equal to (2x + 6)° and x = 7, which statements are true? Check all that apply.

3 lines intersect to form 6 angles. From top left, clockwise, the angles are 1 (90 degrees), 2, 3, 4, 5, 6.
The measure of angle 6 is 20°.
The measure of angle 5 is 70°.
The measure of angle 2 is 80°.
Angles 2 and 5 are complementary.
Angles 5 and 6 are supplementary.
Angles 1 and 4 are supplementary.

Answer 1

Compute angle 3: (2x + 6)° with x = 7 gives 2(7)+6 = 20°, so m∠3 = 20°.

Vertical (opposite) angles are equal, so m∠6 = m∠3 = 20°. Also the three opposite pairs give 1 = 4, 2 = 5, 3 = 6. Since 1 + 2 + 3 = 180° and 1 = 90°, we get 2 + 20 = 90 ⇒ 2 = 70°, hence 5 = 70°.

Therefore the true statements are:
- The measure of angle 6 is 20°.
- The measure of angle 5 is 70°.
- Angles 1 and 4 are supplementary.

The other statements are false.