Question

The sum of two angles of a triangle is 116 and thier difference is 24. find the measures of each angle of/a triangle

Answer 1

Hello

Let there be a triangle ABC with angles A, B and C (as shown in attachment)

Now
Given that
Sum of two angles in 116
Or B+C = 116...... (1)

Also,the difference is 24
So, B - C = 24.....(2)

So,
We get two equations,
By adding the two equations we get...

$b + c = 116 \\ b - c = 24 \\ = = = = = = = = = \\ 2b \: \: \: \: \: = 140 \\ b = \frac{140}{2} = 70$
So
B=70 degrees.
Now,
From equation 1 we get
C= 116 - B
C = 116 - 70 =46 degrees

Now,
We know that
A+B+C =180
A = 180 - (B+C)
A =180 - 116 = 64 degrees

Hope this will be helping you ✌️