7. The sum of two angles of a triangle is 116° and their difference is 24°
Find the measure of each angle of the triangle.
Answers
ANSWER
We shall name the three angles a and b and c
Assuming a and b are the given angles here,
A+B = 116 degrees
A-B = 24 Degrees
2A = 116+24 degrees
= 140 degrees
A = 70 degrees
B = 46 degrees
Third angle = 180 - 70 -46 =64 degrees
Hence the three angles are 70 degrees, 46 degrees and 64 degree
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Answer:
Let us consider the sum of two angles as ∠A+∠B=116° and the difference can be written as ∠A−∠B= 24
We know that the sum of all the angles in a triangle is 180°
So we can write it as :
∠A+∠B+∠C=180°
By substituting ∠A+∠B=116° in the above equation
116°
+ ∠C=180°
On further calculation
:
∠C= 180° − 116°
By subtraction
∠C=64°
It is given that ∠A−∠B=24°
It can be written as ∠A=24° +∠B
Now by substituting ∠A=24° +∠Bin∠A+∠B=116°
∠A+∠B=116°
24° +∠B+∠B=116°
On further calculation
24°
+2∠B=116 °
By subtraction
:
2∠B=116° −24 °
2∠B=92°
By division
:
∠B= 92/2
∠B=46°
By substituting ∠B=46° in ∠A=24° +∠B
We get
:
∠A=24° +46°
By addition:
∠A=70°
Therefore, ∠A=70 ° ,∠B=46° and ∠C=64°
Hope this helps you!