Question

Angle ACD is supplementary to angles ACE and BCD and congruent to angle BCE.

2 lines intersect. Lines D E and A B intersect at point C.
Which statements are true about the angles in the diagram? Select three options.

Angle ACE is supplementary to angle BCD.
Angle BCE is supplementary to angle ACE.
Angle BCD is supplementary to angle BCE.
Angle ACE is congruent to angle BCE.
Angle BCD is congruent to angle ACE.Triangle ABC is a right triangle.

Triangle A B C is a right triangle. Angle A C B is 90 degrees, angle C B A is 31 degrees, and angle B A C is 59 degrees.
What is the relationship between angles A and B?

They are congruent.
They are complementary.
They are supplementary.
There is no relationship between them.Points A, B, and C are on line AC.

A horizontal line has points A, B, C. A line extends from point B up and to the left to point D. Angle D B C is 140 degrees.
Angle CBD has a measure of 140°. What is the measure of angle ABD?

40°
50°
60°
70°Angle B measures 60°. What is the measure of the angle that is complementary to angle B?

30°
60°
120°
180°Angles 1 and 2 form a right angle.

2 lines form a right angle. Another line extends between the 2 lines to form 2 angles. The top angle is labeled 1, and the bottom angle is labeled 2.
Which word describes their measures?

linear
congruent
complementary
supplementaryIn the figure, AngleRQS Is-congruent-to AngleQLK.

3 lines are shown. Lines S P and K N are parallel. Line R M intersects line S P at point Q, and intersects line K N at point L. Angle R Q S is x degrees. Angle K L M is (x minus 36) degrees.
What is the value of x?

36
72
108
144Two lines are intersected by a third line.

Two horizontal parallel lines are intersected by a third line. The third line intersects the top line and forms 4 angles. Labeled clockwise, from uppercase left, the angles are 1, 2, 4, 3. The third line intersects the bottom line and forms 4 angles. Labeled clockwise, from uppercase left, the angles are 5, 6, 8, 7.
If Angle2 Is-congruent-to Angle6, which must be true about Angle2?

Angle2 Is-congruent-to Angle5
Angle2 is complementary to Angle5.
mAngle2 = mAngle8
Angle2 is supplementary to Angle8.Angles A and B are complementary.

Two separate angles are shown. Angle A is (x + 22) degrees. Angle B is x degrees.
What is the value of x?

34
56
68
79Given: Angle1 is complementary to Angle2.
Angle2 is complementary to Angle3.
Prove: mAngle1 = mAngle3
3 separate angles are shown. The angles are labeled 1, 2, 3 from left to right.

A 2-column table with 7 rows. Column 1 is labeled statements with the entries angle 1 is complementary to angle 2, angle 2 is complementary to angle 3, question mark, measure of angle 1 = 90 degrees minus measure of angle 2, measure of angle 2 + measure of angle 3 = 90 degrees, measure of angle 3 = 90 degrees minus measure of angle 2, measure of angle 1 = measure of angle 3. Column 2 is labeled reasons with the entries given, given, definition of complementary angles, subtraction equality property, definition of complementary angles, subtraction equality property, transitive property.

What is the missing statement in step 3 of the proof?

mAngle1 = mAngle2
mAngle1 + mAngle2 = 90°
mAngle2 = mAngle3
mAngle2 + mAngle3 = 180°Right angle FCD intersects Line A B and Ray C E at point C. AngleFCE is congruent to AngleECD. AngleECD is complementary to AngleDCB.

A horizontal line has points A, C, B. Right angle F C D intersects the line at point C. A line extends from point C vertically to point E. Angle A C F is 45 degrees and angle F C D is 90 degrees.
Which statement is true about AngleDCB and AngleACF?

They are congruent and complementary.
They are congruent and supplementary.
They are complementary but not necessarily congruent.
They are supplementary but not necessarily congruent.

Answer 1

Here are the answers with brief justifications:

1) Given: ∠ACD is supplementary to ∠ACE and ∠BCD, and ∠ACD ≅ ∠BCE.
Select three true statements:
- Angle BCE is supplementary to angle ACE. (True, because BCE = ACD and ACD + ACE = 180.)
- Angle BCD is supplementary to angle BCE. (True, because BCE = ACD and ACD + BCD = 180.)
- Angle BCD is congruent to angle ACE. (True, both are supplementary to the same angle ACD so they have equal measures.)

(So choices 2, 3, and 5 are true.)

2) Triangle ABC is right with ∠ACB = 90°, ∠CBA = 31°, ∠BAC = 59°. Relationship between angles A and B?
- They are complementary. (59° + 31° = 90°)

3) Points A, B, C collinear. ∠CBD = 140°. Find ∠ABD.
- 40°. (∠CBD + ∠ABD = 180° along the straight line, so ∠ABD = 180° − 140° = 40°)

4) ∠B = 60°. Measure of angle complementary to ∠B?
- 30° (90° − 60° = 30°)

5) Angles 1 and 2 form a right angle (sum 90°). Their measures are:
- complementary.

6) In the figure with parallel lines SP ∥ KN and transversal RM: ∠RQS = x, ∠KLM = x − 36. Find x.
- 108°. (∠RQS ≅ ∠QLK and ∠QLK and ∠KLM are supplementary at L, so x + (x − 36) = 180 → x = 108.)

7) Two parallel lines cut by a transversal; if ∠2 ≅ ∠6, which must be true about ∠2?
- m∠2 = m∠8. (∠6 and ∠8 are vertical angles, so ∠2 = ∠6 = ∠8.)

8) Angles A and B are complementary. A = x + 22, B = x. Find x.
- 34. (x + (x + 22) = 90 → 2x = 68 → x = 34)

9) Missing statement in the proof (given: ∠1 comp. ∠2, ∠2 comp. ∠3; step 3 reason = definition of complementary angles):
- m∠1 + m∠2 = 90°.

10) Given diagram: ∠FCE ≅ ∠ECD and ∠ECD is complementary to ∠DCB; with ∠ACF = 45° and ∠FCD = 90°. Which is true about ∠DCB and ∠ACF?
- They are congruent and complementary. (Both measure 45°, so equal and sum to 90°.)