Angle Sum Property of a triangle is a fundamental idea in geometry, which states that the sum of the internal angles of a triangle is always 180 degrees.

In this article, we have covered Angle Sum Property of a Triangle, its Practice Worksheet and others in detail.

What is Angle Sum Property of a Triangle?

Angle Sum Property of a Triangle, states that the sum of all internal angles of a triangle is equal to 180^o. Whether a triangle is scalene, isosceles, or equilateral, this feature applies to all of them. Knowing this feature is essential for resolving a wide range of geometric issues and establishing increasingly intricate theorems.

The sum of all internal angles of a triangle is equal to 180^o.

Angle Sum Property of a Triangle is used to:

• Calculate the unknown angles, if we know the other angles in a triangle.
• Confirm that a shape is indeed a triangle.

Important Formulas / Concepts

The exterior angle theorem states that the measurements of a triangle’s two non-adjacent inner angles add up to the outer angle. Mathematically it can be represented as:

• Exterior Angle = Opposite Angle 1 + Opposite Angle 2
• Sum of All Angles of Triangles = 180°

Practice Worksheet Angle Sum Property of a Triangle

Q1. In triangle DEF, if ∠D = 40° and ∠E = 100°, find ∠F.

Q2. In triangle GHI, if ∠G = 35° and ∠H = 65°, find ∠I.

Q3. In triangle JKL, if ∠J = 55° and ∠K = 85°, find ∠L.

Q4. In triangle MNO, if ∠M = 30° and ∠N = 100°, find ∠O.

Q5. In triangle ABC, if ∠A = 50° and ∠B = 60°, find ∠C.

Q6. In triangle XYZ, if ∠X = 80° and ∠Y = 70°, find ∠Z.

Q7. In triangle PQR, if ∠P = 90° and ∠Q = 45°, find ∠R.

Q8. Find the measure of all angles in an equilateral triangle.

Q9. In a triangle, A = 45^o and B = 75^o. Find angle C.

Q10. A triangle has angles A and B such that A=3B. If angle C=30^o, find angles A and B.

Q11. In an isosceles triangle, the two equal angles are 50^o. Find the third angle.

Q12. Find the measure of each angle in an equilateral triangle.

Angle Sum Property of a Triangle Examples with Solution

Example 1: In triangle XYZ , if ∠X = 50^o , ∠Y = 60^o , find ∠Z.

Solution:

Using the angle sum property,

∠X + ∠Y + ∠Z = 180^o

∠Z = 180^o – (∠X + ∠Y)

∠Z = 180^o – ( 50^o + 60^o )

∠Z = 180^o – (110^o)

∠Z = 70^o

Example 2: In triangle ABC , if ∠A = 100^o , ∠B = 30^o , find ∠C.

Solution:

Using the angle sum property,

∠A + ∠B + ∠C = 180^o

∠C = 180^o – (∠A + ∠B)

∠C = 180^o – ( 100^o + 30^o )

∠C = 180^o – (130^o)

∠C = 50^o

Example 3: In triangle PQR , if ∠P = 35^o , ∠Q = 65^o , find ∠R.

Solution:

Using the angle sum property,

∠P + ∠Q + ∠R = 180^o

∠R = 180^o – (∠P + ∠Q)

∠R = 180^o – (35^o + 65^o)

∠R = 180^o – (100)

∠R = 80^o

Example 4: In a given triangle ABC, if all angles are equal. Find measure of each angle.

Solution:

Using the angle sum property,

∠A + ∠B + ∠C = 180^o

(Given all angles are equal)

Let’s suppose ∠A = ∠B = ∠C = x^o

Now ,

x + x + x = 180^o

3x = 180^o

x = 60^o

Measure of each angle=60^o .

All angles are equal to 60^o. This is an equilateral triangle.

Example 5: In an isosceles triangle STU, angles S and T are equal, and angle U = 40 degrees. Find angles S and T.

Solution:

Using the angle sum property,

Let’s suppose ∠S = ∠T = x^o

∠S + ∠T + ∠U = 180

x + x + 40 = 180 (Given, ∠U=40)

2x + 40 = 180

2x = 140

x = 70

So, angles ∠S and ∠T are 70 degrees each

Frequently Asked Questions

Why is Angle Sum Property Significant?

The angle sum property is commonly used in many geometric proofs and problem solving situations, and it is essential for comprehending geometry’s fundamental ideas.

Is it Possible to Apply Angle Sum Property to Every Triangle?

Yes ,it is possible to apply the angle sum property to every triangle, whether a triangle is acute, obtuse, or right-angled, the angle sum characteristic still holds true.

Is it Possible to Determine Unknown Angles in a Triangle using Angle Sum Property?

Yes, when the other angles in the triangle are known, the angle sum feature is frequently employed to find unknown angles.