High school Math aid » Geometry » plane Geometry » triangle » Acute / Obtuse triangles » how to uncover an angle in an acute / obtuse triangle

A triangle has angles the measure 

*
 and 
*
 degrees. What is the measure up of its 3rd angle?


*
 degrees


*
 degrees


*
 degrees


*
 degrees


Explanation:

The sum of the angle of any type of triangle is always 

*
 degrees. Since the third angle will consist of the difference between 
*
 and the amount of the various other two angles, add the various other two angles together and also subtract this sum from 
*
.

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Sum of the two provided angles: 

*
 degrees

Difference between 

*
 and this sum: 
*
 degrees


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

A (Angle A = 41°)

*

B C

 


Explanation:

If angle A is 41°, climate angle C must likewise be 41°, because AB=BC. So, the amount of these 2 angles is:

41° + 41° = 82°

Since the amount of the angle in a triangle is 180°, you can discover out the measure of the continuing to be angle by subtracting 82 from 180:

180° - 82° = 98°

 

 


Explanation:

Recall the the amount of the angle of a triangle is

*
 degrees. Due to the fact that we are provided two angles, we can then find the third. Contact our lacking angle
*

*

We combine the choose terms on the left. 

*

Subtract

*
 from both sides.

*

Thus, we have that our missing angle is

*
 degrees. 

 

 


Explanation:

We recognize that the sum of the angle of a triangle must add up to

*
 degrees. The two given angles amount to
*
 degrees. Thus, a triangle cannot be formed.


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


Explanation:

To solve this question, you need to remember the the amount of the angle in a triangle is 180°. You likewise need to remember supplementary angles. If you know what ∠ DCE is, you likewise know what ∠ ECA is. Thus you recognize two angle of the triangle, 180°-80°-50°= 50°. 


If the typical (arithmetic mean) of two noncongruent angles of one isosceles triangle is

*
, which of the adhering to is the measure up of one of the angle of the triangle?


Explanation:

Since the triangle is isosceles, we recognize that 2 the the angles (that amount up to 180) need to be equal. The question states that the noncongruent angles average 55°, thus offering us v a device of two equations:

*

*

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

70 + 70 + 40 equates to 180 additionally checks out.

Since 70° is not an answer selection for us, we recognize that the 40° have to be among the angles.


*

Points A, B, and C room collinear (they lie follow me the very same line). The measure of edge CAD is

*
. The measure of angle CBD is
*
. The size of segment
*
is 4.


Explanation:

The measure up of 

*
is
*
. Because
*
,
*
, and 
*
space collinear, and the measure of 
*
is
*
, we know that the measure up of 
*
is
*
.

Because the steps of the three angles in a triangle must add up come

*
, and also two that the angles in triangle 
*
are 
*
and
*
, the third angle,
*
, is
*
.


Explanation:

Every triangle has 180 degrees. One isosceles triangle has one vertex angle and also two congruent basic angles. 

Solve the equation

*
because that x to uncover the measure of the vertex angle. 

x = 180 - 27 - 27

x = 126

Therefore the measure up of the vertex angle is

*
.

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