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One interior angle of a triangle has a measure that is equal to the sum of the measures of the other two angles of the triangle. What is the measure of the smallest exterior angle of the triangle in degrees?

 

helpp meeeeee

 Jun 5, 2019

Best Answer 

 #2
avatar+8778 
+3

Let  a  and  b  be the measures of the two other angles of the triangle.

 

the sum of the interior angles in a triangle  =  180°

 

a + b + (a + b)  =  180°

 

2(a + b)  =  180°

 

a + b  =  90°

 

the measure of the smallest exterior angle  =  180° - the measure of the largest interior angle

 

the measure of the smallest exterior angle  =  180° - ( a + b )

 

the measure of the smallest exterior angle  =  180° - 90°

 

the measure of the smallest exterior angle  =  90°

 Jun 6, 2019
 #1
avatar+342 
0

There are a theorem witch say:

An exterior angle of a triangle is equal to the sum of the other two angles of the triangle.

 

So the measure of the smallest exterior angle of the triangle equals to the sum of the other two angles of the triangle.

 Jun 5, 2019
edited by Dimitristhym  Jun 5, 2019
edited by Dimitristhym  Jun 5, 2019
 #2
avatar+8778 
+3
Best Answer

Let  a  and  b  be the measures of the two other angles of the triangle.

 

the sum of the interior angles in a triangle  =  180°

 

a + b + (a + b)  =  180°

 

2(a + b)  =  180°

 

a + b  =  90°

 

the measure of the smallest exterior angle  =  180° - the measure of the largest interior angle

 

the measure of the smallest exterior angle  =  180° - ( a + b )

 

the measure of the smallest exterior angle  =  180° - 90°

 

the measure of the smallest exterior angle  =  90°

hectictar Jun 6, 2019
 #3
avatar+104627 
+1

Nice, hectictar   !!!!

 

 

cool cool cool

CPhill  Jun 6, 2019

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