High School Math : Acute / Obtuse Triangles

Study concepts, example questions & explanations for High School Math

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Example Questions

Example Question #16 : How To Find An Angle In An Acute / Obtuse Triangle

Rt_triangle_lettersIf angle  and angle , what is the value of ?

Possible Answers:

Correct answer:

Explanation:

For this problem, remember that the sum of the degrees in a triangle is .

This means that .

Plug in our given values to solve:

Example Question #17 : How To Find An Angle In An Acute / Obtuse Triangle

In , and . To the nearest tenth, what is  ?

Possible Answers:

A triangle with these sidelengths cannot exist.

Correct answer:

A triangle with these sidelengths cannot exist.

Explanation:

The sum of the two smallest sides is less than the greatest side:

By the Triangle Inequality, this triangle cannot exist.

Example Question #18 : How To Find An Angle In An Acute / Obtuse Triangle

Exterior_angle

 

If the measure of  and the measure of  then what is the meausre of ?

Possible Answers:

Not enough information to solve

Correct answer:

Explanation:

The key to solving this problem lies in the geometric fact that a triangle possesses a total of  between its interior angles.  Therefore, one can calculate the measure of  and then find the measure of its supplementary angle, .

 and  are supplementary, meaning they form a line with a measure of .

One could also solve this problem with the knowledge that the sum of the exterior angle of a triangle is equal to the sum of the two interior angles opposite of it.

Example Question #19 : How To Find An Angle In An Acute / Obtuse Triangle

Exterior_angle

 

 

If the measure of  and the measure of  then what is the meausre of ?

Possible Answers:

Not enough information to solve

Correct answer:

Explanation:

The key to solving this problem lies in the geometric fact that a triangle possesses a total of  between its interior angles.  Therefore, one can calculate the measure of  and then find the measure of its supplementary angle, .

 and  are supplementary, meaning they form a line with a measure of .

One could also solve this problem with the knowledge that the sum of the exterior angle of a triangle is equal to the sum of the two interior angles opposite of it.

Example Question #861 : High School Math

A triangle has angles that measure  and  degrees. What is the measure of its third angle?

Possible Answers:

 degrees

 degrees

 degrees

 degrees

 degrees

Correct answer:

 degrees

Explanation:

The sum of the angles of any triangle is always  degrees. Since the third angle will make up the difference between  and the sum of the other two angles, add the other two angles together and subtract this sum from .

Sum of the two given angles:  degrees

Difference between  and this sum:  degrees

Example Question #166 : Plane Geometry

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:

82

98

41

90

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 #862 : High School Math

You are given a triangle with angles  degrees and  degrees. What is the measure of the third angle? 

Possible Answers:

 degrees 

 degrees

 degrees 

 degrees

 degrees

Correct answer:

 degrees

Explanation:

Recall that the sum of the angles of a triangle is  degrees. Since we are given two angles, we can then find the third. Call our missing angle

We combine the like terms on the left. 

Subtract  from both sides.

Thus, we have that our missing angle is  degrees. 

 

 

Example Question #863 : High School Math

What is the third angle in a triangle with angles of  degrees and  degrees? 

Possible Answers:

No such triangle can exist.

 degrees 

 degrees 

 degrees 

 degrees 

Correct answer:

No such triangle can exist.

Explanation:

We know that the sum of the angles of a triangle must add up to  degrees. The two given angles sum to  degrees. Thus, a triangle cannot be formed.

Example Question #171 : Plane Geometry

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°

80°

60°

50°

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 #13 : Isosceles Triangles

If the average (arithmetic mean) of two noncongruent angles of an isosceles triangle is , which of the following is the measure of one of the angles of the triangle?

Possible Answers:

Correct answer:

Explanation:

Since the triangle is isosceles, we know that 2 of the angles (that sum up to 180) must be equal. The question states that the noncongruent angles average 55°, thus providing us with a system of two equations:

Solving for x and y by substitution, we get x = 70° and y = 40° (which average out to 55°).

70 + 70 + 40 equals 180 also checks out.

Since 70° is not an answer choice for us, we know that the 40° must be one of the angles.

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