Question

Calculate the value of a. (Image Attached)

Answer 1

Answer-75°

step by step explanation is given in the image attached.

Answer 2

Answer :-

• The value of a° = 75°.

To find :-

• The value of a.

Step-by-step explanation :-

• To find the value of a°, we first have to find the value of x. We will later see why!

• Before that, let's find the value of x.

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$\mid \underline{\boxed{ \sf To \: find \: the \: value \: of \: x :-}} \mid$

• Let an unknown angle be x.

• As we can see in the figure, x is a part of a triangle.

• In this triangle, we know the values of the other two angles.

Here,

• First angle = 45°.
• Second angle = 60°.

• We have to find the third angle, which is x.

We know that :-

$\underline{\boxed{\sf Sum \: of \: all \: the \: angles \: in \: a \: triangle = 180^{\circ}.}}$

• So, the three angles of this triangle must add up to 180°.

$\tt \implies x + 45^{\circ} + 60^{\circ} = 180^{\circ}$

Adding 45° and 60°,

$\tt \implies x + 105^{\circ} = 180^{\circ}$

Transposing 105° from LHS to RHS, changing it's sign,

$\tt \implies x = 180^{\circ} - 105^{\circ}$

Subtracting 105° from 180°,

$\tt \implies x = 75^{\circ}.$

• The value of x = 75°.

So, let's find the value of a° using x.

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$\mid \underline{\boxed{ \sf To \: find \: the \: value \: of \: a^{\circ} :-}} \mid$

• Now, as we can see in the figure, a° and x are vertically opposite angles.

We know that :-

$\underline{\boxed{\sf Vertically \: opposite \: angles \: are \: equal.}}$

• So, that means x = a°.

• And x = 75°.

• Therefore, a° = 75°.

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• Note :- Kindly see the attachment for better understanding.