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A triangle has actually angles that measure 

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


*
 degrees


*
 degrees


*
 degrees


*
 degrees


Explanation:

The sum of the angle of any triangle is always 

*
 degrees. Due to the fact that the third angle will comprise the distinction 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 no to scale) . If angle A is 41°, what is the measure of edge B?

A (Angle A = 41°)

*

B C

 


Explanation:

If edge A is 41°, then angle C must likewise 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°, friend can discover out the measure of the continuing to be angle by individually 82 native 180:

180° - 82° = 98°

 

 


Explanation:

Recall the the amount of the angles of a triangle is

*
 degrees. Because we are given two angles, we deserve to then find the third. Contact our absent angle
*
. 

*

We combine the choose terms on the left. 

*

Subtract

*
 from both sides.

*

Thus, we have that our lacking angle is

*
 degrees. 

 

 


Explanation:

We know that the amount of the angles 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 space collinear. The measure up of ∠ DCE is 130° and of ∠ AEC is 80°. Discover the measure of ∠ EAD.


Explanation:

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


If the average (arithmetic mean) of 2 noncongruent angles of an isosceles triangle is

*
, i beg your pardon 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 that the angles (that amount up to 180) need to be equal. The concern states the the noncongruent angles median 55°, thus offering us with a mechanism of two equations:

*

*

Solving because that x and also y by substitution, we obtain x = 70° and y = 40° (which median out to 55°).

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

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


*

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

*
. The measure of edge CBD is
*
. The length of segment
*
is 4.


Explanation:

The measure of 

*
is
*
. Because
*
,
*
, and 
*
room collinear, and the measure up of 
*
is
*
, we recognize that the measure up of 
*
is
*
.

Because the actions of the 3 angles in a triangle must include up come

*
, and also two of the angle in triangle 
*
are 
*
and
*
, the 3rd angle,
*
, is
*
.

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Explanation:

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

Solve the equation

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

x = 180 - 27 - 27

x = 126

Therefore the measure of the vertex angle is

*
.


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