Question

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Answer 1

Required answer:-

Question:

1. The three angles are 57⁰, 62⁰ and 61⁰ verify the angle sum property for this triangle.

2. One of the angle of a triangle is equal to the sum of the other two equal angles. What is the angle?

Solution:

1. Given,

• Measure of three angles of a triangle = 57⁰, 62⁰, and 61⁰.

To find:

• Verify angle sum property

Concept:

• Triangles

Step by step explaination:

As we know measure of all the sides of a triangle is 180⁰.

Let a ∆ABC in which ∠A = 62⁰ , ∠B = 57⁰ , C= 61⁰

∠A + ∠B + ∠C = 180⁰

62⁰ + 57⁰ + 61⁰ = 180⁰

Thus angle sum property of this triangle is verified.

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2. Given,

• One angle of a triangle is equal to the sum of the other two angles.

To find:

• Measure of the first angle

Assumptions:

• Measure of first angle = x

• Measure of the second angle = y

• Measure of the third angle = z

Step by step explaination:

According to the question one angle is equal to the sum of other two angles.

That is,

x = y + z

Now,

As we know

Measure of all the sides of a triangle is 180⁰.

x + y + z = 180⁰

x + x = 180⁰

$2x = 180⁰$

x = 90⁰

Answer:

Required angle is of 90⁰

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More information:

Triangle:

A plane figure bounded by three straight line segments, is called a triangle. Every triangle has three vertices and three sides.

Relation between sides and angles of a triangle:

1. If all the sides of a triangle are of different lengths, it's angles are also of different measures in such a way that, the greater angle has greater angle opposite to it.

2. If any two angles of a triangle are equal, the angles opposite to them are also equal.

3. Conversely, if all the angles of a triangle have different measures, its sides are also of different lengths in such a way that the greater angle has greater side opposite to it.

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