Question

the sum of the two angles of a triangle is 116and their difference is 24.Find the measure of each angle of a triangle​

Answer 1

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Measure of all the three angles of triangle will be :

46° , 64° and 70°

Solution

As we know that sum of interior angles of∆ is 180°

Let the angles of triangle as a , b and c

We have been provided in the question that.

Sum of two angles of triangle is 116 and the difference of these two angles is 24°

So , mathematically we can write it as

a+b = 116°. ( 1)

a-b = 24. (2)

Now Substracting eq 1and 2.

a+b -(a-b) = 116 - 24

On opening the bracket we will change the sign according to mathematics rules.

Calculation

a+b - a + b = 92

2b = 92

b = 92/2

b = 46°

Now adding eq 1 and 2 we get

a + b + a - b = 116 +24

2a = 140

a = 140/2

a = 70°

Now applying interior angle sum property.

a + b + c = 180°

70 + 46 + c = 180

c = 180 - 116

c = 64°

Verification

a + b = 116

putting the value of a and b

70 + 46 = 116

a - b = 24

Again putting value of a and b.

70 - 46 = 24°

Hence verified

Answer 2

GIVEN :

Sum of two angles of a traingle = 116°

Difference of those two angles = 24°

Third angle = 180° - 116° = 64°

Let the angles be x and y

x + y = 116

x - y = 24

---------------

2x = 140

x = 140/2

x = 70°

Substitute x in any equation

x + y = 116

70 + y = 116

y = 116 - 70

y = 46°

Therefore, the two angles are 70° and 46°