ACT Math : How to find an angle in an acute / obtuse triangle

Study concepts, example questions & explanations for ACT Math

Example Questions

Example Question #1 : How To Find An Angle In An Acute / Obtuse Triangle

Two interior angles in an obtuse triangle measure 123^{\circ} and 11^{\circ}. What is the measurement of the third angle. 

Possible Answers:

46^{\circ}

50^{\circ}

57^{\circ}

104^{\circ}

123^{\circ}

Correct answer:

46^{\circ}

Explanation:

Interior angles of a triangle always add up to 180 degrees. 

Example Question #2 : How To Find An Angle In An Acute / Obtuse Triangle

In a given triangle, the angles are in a ratio of 1:3:5.  What size is the middle angle?

Possible Answers:

45^{\circ}

90^{\circ}

20^{\circ}

75^{\circ}

60^{\circ}

Correct answer:

60^{\circ}

Explanation:

Since the sum of the angles of a triangle is 180^{\circ}, and given that the angles are in a ratio of 1:3:5, let the measure of the smallest angle be , then the following expression could be written:

x+3x+5x=180

9x=180

x=20

 

If the smallest angle is 20 degrees, then given that the middle angle is in ratio of 1:3, the middle angle would be 3 times as large, or 60 degrees.

Example Question #3 : How To Find An Angle In An Acute / Obtuse Triangle

In the triangle below, AB=BC (figure is not to scale) .  If angle A is 41°, what is the measure of angle B?

                                       A (Angle A = 41°)

                                       Act_math_108_02               

                                     B                           C

 

Possible Answers:

90

82

98

41

Correct answer:

98

Explanation:

  If angle A is 41°, then angle C must also be 41°, since AB=BC.  So, the sum of these 2 angles is:

41° + 41° = 82°

Since the sum of the angles in a triangle is 180°, you can find out the measure of the remaining angle by subtracting 82 from 180:

180° - 82° = 98°

 

 

Example Question #4 : How To Find An Angle In An Acute / Obtuse Triangle

Points A, B, C, D are collinear. The measure of ∠ DCE is 130° and of ∠ AEC is 80°. Find the measure of ∠ EAD.

Screen_shot_2013-03-18_at_3.27.08_pm

Possible Answers:

70°

50°

60°

80°

Correct answer:

50°

Explanation:

To solve this question, you need to remember that the sum of the angles in a triangle is 180°. You also need to remember supplementary angles. If you know what ∠ DCE is, you also know what ∠ ECA is. Hence you know two angles of the triangle, 180°-80°-50°= 50°. 

Example Question #5 : How To Find An Angle In An Acute / Obtuse Triangle

Triangles

Points A, B, and C are collinear (they lie along the same line). The measure of angle CAD is 30^{\circ}. The measure of angle CBD is 60^{\circ}. The length of segment \overline{AD} is 4.

Find the measure of \dpi{100} \small \angle ADB.

Possible Answers:

30^{\circ}

60^{\circ}

45^{\circ}

15^{\circ}

90^{\circ}

Correct answer:

30^{\circ}

Explanation:

The measure of \dpi{100} \small \angle ADB is 30^{\circ}. Since \dpi{100} \small A, \dpi{100} \small B, and \dpi{100} \small C are collinear, and the measure of \dpi{100} \small \angle CBD is 60^{\circ}, we know that the measure of \dpi{100} \small \angle ABD is 120^{\circ}.

Because the measures of the three angles in a triangle must add up to 180^{\circ}, and two of the angles in triangle \dpi{100} \small ABD are 30^{\circ} and 120^{\circ}, the third angle, \dpi{100} \small \angle ADB, is 30^{\circ}.

Learning Tools by Varsity Tutors