Question

Step 1 of 3: Find the measure of 23.

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rev
cung straight lin
AnswerHow to enter your answer (opens in new window) 2 Points
y
x, y, and z, with mzl
2
3
4
6
5
57 and m≥6 = 90

Answer 1

• ∠1 = ∠4 = 57°
• ∠2 = ∠5 = 33°
• ∠3 = ∠6 = 90°

Explanation:

You want the measures of the numbered angles in the figure, where angle 6 is 90°, and adjacent angle 1 is 57°.

Vertical angles

Vertical angles are congruent. The vertical angle pairs in the figure are ...

• 1 and 4
• 2 and 5
• 3 and 6

Complementary angles

Line y splits the right angles into complementary pairs: 1 and 2, 4 and 5. Complementary angles have a sum of 90°.

Angle measures

Angle 1 is given as 57°. Angle 4 is congruent, so is also 57°.

Angle 2 is complementary to angle 1, so is 90° -57° = 33°. Angle 5 is congruent, so is also 33°.

Angle 3 is given as 90°. Angle 6 is congruent, so is also 90°.

• ∠1 = ∠4 = 57°
• ∠2 = ∠5 = 33°
• ∠3 = ∠6 = 90°