Question

One of the acute angles of a right angled triangle is 42°, Find the other acute angle.
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Answer 1

Answer :-

• The other acute angle is 48°.

Given :-

• One of the acute angles of a right angled triangle is 42°.

To find :-

• The other acute angle.

Step-by-step explanation :-

• In this question, it has been given that one of the acute angles is 42°. We have to find the other acute angle.

We know that :-

$\underline{\boxed{\sf Acute \: angles \: are \: less \: than \: 90^{\circ}}}$

• So, that means the other angle is also less than 90°.

Now,

$\underline{\boxed{\sf A \: right \: angled \: triangle\: has \: one \: side \: of \: 90^{\circ}}}$

• Therefore, it means that two angles in this triangle are 42° and 90°. Now it's easier to find the third angle.

• Let's take the third angle as x.

We know that :-

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

• So, all these angles must add up to 180°.

$\sf\implies x + 42^{\circ} + 90^{\circ} = 180^{\circ}$

Adding 42° and 90°,

$\sf \implies x + 132^{\circ} = 180^{\circ}$

Transposing 132° from LHS to RHS, changing it's sign,

$\sf \implies x = 180^{\circ} - 132^{\circ}$

Subtracting 132° from 180°,

$\sf \implies x = 48^{\circ}.$

• The value of x is 48°.

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Hence, the other acute angle is 48°.

Answer 2

Answer:

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