The Triangle and its Properties worksheet for class 7 | myCBSEguide - Free Printable

To solve the problems in the given images, we need to use properties of triangles, such as the angle sum property and the relationships between angles in specific types of triangles. Let's go through each image step by step.

Image (i)

This is an isosceles triangle with one angle given as \(60^\circ\) and another angle given as \(50^\circ\). We need to find the measure of the third angle \(x\).

1. The sum of the angles in a triangle is \(180^\circ\).
2. The two base angles of an isosceles triangle are equal. Since one of the base angles is \(50^\circ\), the other base angle is also \(50^\circ\).
3. Therefore, the third angle \(x\) can be calculated as:
\[
x = 180^\circ - 50^\circ - 60^\circ = 70^\circ
\]

So, the value of \(x\) is \(\boxed{70}\).

Image (ii)

This is a right triangle with one angle given as \(30^\circ\) and the right angle as \(90^\circ\). We need to find the measure of the third angle \(x\).

1. The sum of the angles in a triangle is \(180^\circ\).
2. The right angle is \(90^\circ\) and one of the other angles is \(30^\circ\).
3. Therefore, the third angle \(x\) can be calculated as:
\[
x = 180^\circ - 90^\circ - 30^\circ = 60^\circ
\]

So, the value of \(x\) is \(\boxed{60}\).

Image (iii)

This is a triangle with one angle given as \(110^\circ\) and another angle given as \(30^\circ\). We need to find the measure of the third angle \(x\).

1. The sum of the angles in a triangle is \(180^\circ\).
2. Therefore, the third angle \(x\) can be calculated as:
\[
x = 180^\circ - 110^\circ - 30^\circ = 40^\circ
\]

So, the value of \(x\) is \(\boxed{40}\).

Image (iv)

This is an isosceles triangle with one angle given as \(50^\circ\) and the other two angles being equal. We need to find the measure of the equal angles \(x\).

1. The sum of the angles in a triangle is \(180^\circ\).
2. Let the two equal angles be \(x\). Then:
\[
x + x + 50^\circ = 180^\circ
\]
3. Simplifying, we get:
\[
2x + 50^\circ = 180^\circ
\]
\[
2x = 130^\circ
\]
\[
x = 65^\circ
\]

So, the value of \(x\) is \(\boxed{65}\).

Image (v)

This is an equilateral triangle, where all three angles are equal. We need to find the measure of each angle \(x\).

1. The sum of the angles in a triangle is \(180^\circ\).
2. Since all three angles are equal in an equilateral triangle:
\[
x + x + x = 180^\circ
\]
\[
3x = 180^\circ
\]
\[
x = 60^\circ
\]

So, the value of \(x\) is \(\boxed{60}\).

Image (vi)

This is a right triangle with one angle given as \(x\) and the other angle given as \(2x\). We need to find the measure of the angle \(x\).

1. The sum of the angles in a triangle is \(180^\circ\).
2. The right angle is \(90^\circ\), so the sum of the other two angles is:
\[
x + 2x = 90^\circ
\]
3. Simplifying, we get:
\[
3x = 90^\circ
\]
\[
x = 30^\circ
\]

So, the value of \(x\) is \(\boxed{30}\).

Final Answers

\[
\boxed{70, 60, 40, 65, 60, 30}
\]