Question

In ∆ABC, ∠A + ∠B = 100° and ∠B + ∠C = 130°. Find the measure of
each angle.

Answer 1

Given :

• ∠A + ∠B = 100°
• ∠C + ∠B = 130°

To Find :

The measure of each angle

Identity of triangle to be used :

We will use the angle sum property of the triangle here to calculate the the Angles .

Angle sum property of triangle say :

• ∠A+∠B+∠C = 180°

To Be Done :

We will first find the value of ∠C because in the first equation, sum of ∠A and ∠B is given .

Then we can calculate the value of ∠A and ∠B from the second equation as we will be knowing the value of ∠C

Let's Go!

Solution :

As in first equation, it is given :

∠A + ∠B = 100° ,

so, using the angle sum property of triangle we get that,

∠A+∠B+∠C = 180°

or, (∠A+∠B)+∠C = 180°

Now, we will substitute the value of ∠A+∠B here,

or, 100° + ∠C = 180°

or, ∠C = 180°-100°

or, ∠C = 80°

Hence, Value of Angle C is 80°

Now, we know the value of ∠C , so from the second equation, we will find the Value of ∠A :

∠A+∠B+∠C = 180°

From the second equation we get that ,

∠A+(∠B+∠C)=180°

or, ∠A+130° = 180°

or, ∠A = 180°-130°

or, ∠A = 50°

So, value of Angle A = 50°

Now, we will substitute the value of ∠A and ∠C in the Angle sum property to find angle B

So, ∠A+∠B+∠C = 180°

or, 50°+∠B+80° = 180°

or, 130°+∠B = 180°

or, ∠B = 180°-130°

or, ∠B = 50°

Hence, the value of Angle B = 50°

So, the value of All the three angles are :

• ∠A = 50°
• ∠B = 50°
• ∠C = 130°

_____________________

Verification :

Now, we will check of we have got the right answers or not .

1] So, first we will substitute the value of ∠A and ∠B in the first equation:

∠A+∠B = LHS

100° = RHS

So, ∠A+∠B = 50°+50°

or, ∠A+∠B = 100°

Hence, LHS = RHS

2] Now, we will Check with second equation:

∠B+∠C = LHS

130° = RHS

So, ∠B+∠C = 50°+80°

or, ∠B+∠C = 130°

Hence, LHS = RHS

3] Now, we will Check with the angle sum property of triangle:

∠A+∠B+∠C = LHS

180°= RHS

So, ∠A+∠B+∠C = 50°+50°+80°

or, ∠A+∠B+∠C = 180°

Hence, LHS = RHS

Hence Verified !

_____________________

Additional Information :

These are some properties and Theorem about triangle:

1] Side opposite to greater angle is always greater

2] Angle opposite to equal side are equal

3] Hypotenuse is the biggest side in Right Angle triangle

4] Pythagorean Theorem says :

Hypotenuse² = Base²+Hieght²

5] In acute angle triangle ABC , which have longest side as AB ,

AB² < BC²+AC²

6] In obtuse angle triangle PQR , which have PQ as longest side,

PQ²> QR²+PR²