Question

please say question no 2 answer

Answer 1

[Answers of 3, 4, 5 and 6 are attached]

★ Solution (1) :-

First, we will find the value of x.

The triangle having the variable x is an isosceles triangle. So, the other unknown angle is 70° itself. So,

Measure of ∠x :-

$\sf \leadsto {70}^{\circ} + {70}^{\circ} + \angle{x} = {180}^{\circ}$

$\sf \leadsto {140}^{\circ} + \angle{x} = {180}^{\circ}$

$\sf \leadsto \angle{x} = 180 - 140$

$\sf \leadsto \angle{x} = {40}^{\circ}$

Now, we can find the value of y.

The triangle having the variable y is also an isosceles triangle. So, the other angle also measures same as y. So,

Measure of ∠y :-

$\sf \leadsto {110}^{\circ} + \angle{y} + \angle{y} = {180}^{\circ}$

$\sf \leadsto {110}^{\circ} + 2y = {180}^{\circ}$

$\sf \leadsto 2y = 180 - 110$

$\sf \leadsto 2y = 70$

$\sf \leadsto y = \dfrac{70}{2}$

$\sf \leadsto \angle{y} = {35}^{\circ}$

Therefore, the measurements of x and y are 40° and 35°

★ Solution (2) :-

We know that the triangle on left is an isosceles triangle. So, one part of x and y can be found now.

$\sf \leadsto {100}^{\circ} + a + a = {180}^{\circ}$

$\sf \leadsto {100}^{\circ} + 2a = {180}^{\circ}$

$\sf \leadsto 2a = 180 - 100$

$\sf \leadsto 2a = 80$

$\sf \leadsto a = \dfrac{80}{2}$

$\sf \leadsto a = 40$

Now, we can find the values of other half part of x and y. We know that the triangle on right is an equilateral triangle. So,

$\sf \leadsto b + b + b = {180}^{\circ}$

$\sf \leadsto 3b = {180}^{\circ}$

$\sf \leadsto b = \dfrac{180}{3}$

$\sf \leadsto b = 60$

Now, we can find the values of x and y.

Measure of ∠x :-

$\sf \leadsto a + b = 40 + 60$

$\sf \leadsto \angle{x} = {100}^{\circ}$

Measure of ∠y :-

$\sf \leadsto a + b = 40 + 60$

$\sf \leadsto \angle{y} = {100}^{\circ}$

Therefore, the measurements of x and y are 100° and 100°.

Answer 2

ANSWERS☟

i) A = 70° (Angles opposite to equal sides)

But a + 70° + x = 180° (Angles of a triangle)

=> 70° + 70° + x = 180°

=> 140° + x = 180°

=> x = 180° – 140° = 40°

∴ ∠x = 40°

y = b (Angles opposite to equal sides)

But a = y + b

(Exterior angle of a triangle is equal to sum of its interior opposite angles).

=> 70° = y + y => 2y = 70°

=> y = 70°/2 = 35°

∴ ∠y = 35°

∴Measurements of x and y are 40° and 35°.

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ii) In a equivalateral triangle,

Each angle = 60°

In an isosceles triangle.,

Let, each base angle = a.

∴ a + a + 100° = 180°

=> 2a + 100° = 180°

=> 2a = 180° – 100° = 80°

∴ a = 80°/2 = 40°,

∴ x = 60° + 40° = 100°

∴ ∠x = 100°

and y = 60° + 40° = 100°

∴ ∠y = 100°

∴Measurements of x and y are 100° and 100°.

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iii) 130° = x + p

(Exterior angle of a triangle is equal to the sum of its interior opposite angles).

∵Lines are parallel (Given)

∴p = 60° = (Alternate angle)

And y = a

But, a + 130° = 180° (Linear Pair)

=> a = 180° – 130° = 50°

∴ ∠y = 50°

And x + p = 130°

=> x + 60° = 130° => x = 130° – 60° = 70°

∴ x = 70°

∴Measurements of x and y are 70° and 50°.

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iv) x = a + b

But, b = y (Angles opposite to equal sides)

Similarly, a = c

But, a + c + 30° = 180°

=> a + a + 30° = 180°

=> 2a + 30° = 180°

=> 2a = 180° – 30° = 150°

=> a = 150°/2 = 75° and b + y = 90°

=> y + y = 90° => 2y = 90°

=> y = 90°/2 = 45°

∴ ∠y = 45°

And x = a + b = 75° + 45° = 120°

∴ ∠x = 120°

∴Measurements of x and y are 120° and 45°.

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v) a + b + 40° = 180° (Angles of a triangle)

=> a + b = 180° – 40° = 140°

But, a = b (Angles opposite to equal sides)

∴ a = b = 140°/2 = 70°

∴ x = b + 40° = 70° + 40° = 110°

∴ ∠x = 110°

(Exterior angle of a triangle is equal to the sum of its interior opposite angles).

Similarly, y = a + 40°

=> 70° + 40° = 110°

∴ ∠y = 110°

∴Measurements of x and y are 110° and 110°.

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vi) a = b (Angles opposite to equal sides)

∴ ∠y = 120°

But, a + 120° = 180° (Linear Pair)

=> a = 180° – 120° = 60°

∴ b = 60°

But, x + a + b = 180° (Angles of a triangle)

=> x + 60° + 60° = 180°

=> x + 120° = 180°

∴ ∠x = 180°

x = 180° – 120° = 60°

B = z + 25°

(Exterior angle of a triangle is equal to the sum of its interior opposite angles).

=> 60° = z + 25°

=> z = 60° – 25° = 35°

∴ ∠z = 35°

∴Measurements of x,y and z are 60°,120°, and 35°.

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Refer Above attachments for diagram.

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