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

Study concepts, example questions & explanations for High School Math

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Example Questions

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

Solve for . (Not drawn to scale).

 

Possible Answers:

Correct answer:

Explanation:

The angles of a triangle must add to 180o. In the triangle to the right, we know one angle and can find another using supplementary angles.

Now we only need to solve for .

Example Question #34 : Triangles

Exterior_angleIf  and , what is the measure of ?

Possible Answers:

Not enough information to solve

Correct answer:

Explanation:

All of the interior angles of a triangle add up to .  

If  and , then 

Therefore,

Now,  will equal because  and  form a straight line.  Therefore,

 

Also, by definition, the angle of an exterior angle of a triangle is equal to the measure of the two interior angles opposite of it .

Example Question #6 : Acute / Obtuse Triangles

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

Possible Answers:

104^{\circ}

46^{\circ}

57^{\circ}

123^{\circ}

50^{\circ}

Correct answer:

46^{\circ}

Explanation:

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

Example Question #311 : Geometry

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

Possible Answers:

90^{\circ}

75^{\circ}

60^{\circ}

45^{\circ}

20^{\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

Triangle ABC has angle measures as follows:

\dpi{100} \small m\angle ABC=4x+3 

\dpi{100} \small m\angle ACB=2x+6

\dpi{100} \small m\angle BAC=3x

What is \dpi{100} \small m\angle BAC?

Possible Answers:

57

90

44

19

79

Correct answer:

57

Explanation:

The sum of the measures of the angles of a triangle is 180.

Thus we set up the equation \dpi{100} \small 4x+3+2x+6+3x=180

After combining like terms and cancelling, we have \dpi{100} \small 9x=171\rightarrow x=19

Thus \dpi{100} \small m\angle BAC=3x=57

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

The base angle of an isosceles triangle is five more than twice the vertex angle.  What is the base angle?

Possible Answers:

34

47

62

55

73

Correct answer:

73

Explanation:

Every triangle has 180 degrees.  An isosceles triangle has one vertex angle and two congruent base angles.

Let x = the vertex angle and 2x+5 = the base angle

So the equation to solve becomes  x+(2x+5)+(2x+5)=180

Thus the vertex angle is 34 and the base angles are 73.

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

The base angle of an isosceles triangle is 15 less than three times the vertex angle.  What is the vertex angle?

Possible Answers:

Correct answer:

Explanation:

Every triangle contains 180 degrees.  An isosceles triangle has one vertex angle and two congruent base angles.

Let  = vertex angle and  = base angle

So the equation to solve becomes .

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

The base angle of an isosceles triangle is ten less than twice the vertex angle.  What is the vertex angle?

Possible Answers:

Correct answer:

Explanation:

Every triangle has 180 degrees.  An isosceles triangle has one vertex angle and two congruent base angles.

Let  = vertex angle and  = base angle

So the equation to solve becomes 

So the vertex angle is 40 and the base angles is 70

Example Question #7 : How To Find An Angle In An Acute / Obtuse Triangle

The base angle of an isosceles triangle is 10 more than twice the vertex angle.  What is the vertex angle?

Possible Answers:

Correct answer:

Explanation:

Every triangle has 180 degrees.  An isosceles triangle has one vertex angle and two congruent base angles.

Let = the vertex angle and  = the base angle

So the equation to solve becomes

The vertex angle is 32 degrees and the base angle is 74 degrees

Example Question #11 : Isosceles Triangles

In an isosceles triangle, the vertex angle is 15 less than the base angle.  What is the base angle?

Possible Answers:

Correct answer:

Explanation:

Every triangle has 180 degrees.  An isosceles triangle has one vertex angle and two congruent base angles.

Let  = base angle and  = vertex angle

So the equation to solve becomes

Thus, 65 is the base angle and 50 is the vertex angle.

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