Question

Pls answer these questions:
Q . Out of a pair of complementary angles, one is 2/3 of the other. Find the angles.
Q . Measures of two supplementary angles are consecutive odd integers. Find the angles.

Answer 1

Question 1 :-

• Out of a pair of complementary angles, one is 2/3 of the other. Find the angles.

Answer :-

• The complementary angles are 36° and 54°.

To find :-

• The complementary angles.

Step-by-step explanation :-

• Let one of the angles be "x".

It is given that :-

• The other angle is 2/3 of the first angle.

Then :-

• $\rm The \: other \: angle \: will \: be \: \dfrac{2}{3} x$

We know that :-

$\underline{ \boxed{\sf Complementary \: angles \: add \: up \: to \: 90^{\circ}}}$

Therefore,

$\rm{\longrightarrow \: \dfrac{2}{3}x + x = 90}$

$\longrightarrow \rm \dfrac{2x}{3} + x = 90$

$\rm \longrightarrow \dfrac{2x \times 1 + x \times 3}{3} = 90$

$\rm \longrightarrow \dfrac{2x + 3x}{3} = 90$

$\rm{\longrightarrow \: \dfrac{5x}{3} = 90}$

$\rm{\longrightarrow \: 5x = 90 \times 3}$

$\rm{\longrightarrow \: 5x = 270}$

$\rm{\longrightarrow \: x = \cancel{\dfrac{270}{5}}}$

$\rm{\longrightarrow \: x = 54}$

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Hence, the angles are :-

$\bf x = 54^{ \circ} .$

$\bf\dfrac{2}{3} x = \dfrac{2}{3} \times 54 = 36^{ \circ} .$

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Question 2 :-

• Measures of two supplementary angles are consecutive odd integers. Find the angles.

Answer :-

• The angles are 89° and 91°.

To find :-

• The angles.

Step-by-step explanation :-

• Let the two consecutive odd integers be (x)° and (x+2)°.

We know that :-

$\underline{ \boxed{\sf Supplementary \: angles \: add \: up \: to \: 180^{\circ}}}$

Therefore,

$\longrightarrow \: \rm{x + x + 2 = 180}$

$\longrightarrow \: \rm{2x + 2 = 180}$

$\longrightarrow \: \rm{2x = 180 - 2}$

$\longrightarrow \: \rm{2x = 178}$

$\longrightarrow \: \rm{x = \cancel{\dfrac{178}{2}}}$

$\longrightarrow \: \rm{x = 89}$

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Hence, the angles are :-

$\bf x = 89^{ \circ} .$

$\bf x + 2 = 89^{ \circ} + 2 = 91^{ \circ} .$