Question

7. Two angles are complementary. The larger angle is 3° less than twice the me
smaller angle. Find the measure of each angle.​

Answer 1

Given :–

• Two angles are complementary.
• The larger angle is 3° less that the mesures of the smaller angle.

To Find :–

• The measure of each angle.

Solution :–

Let,

The measure of larger angle be x.

And the measure of smaller angle be y.

According to the question,

The larger angle is 3° less than the measure of the smaller angle.

So the equation is,

⟹ x = 2y – 3

We know that,

Complementary angle = 90°

So,

⟹ x + y = 90°

here,

• x = 2y – 3

⟹ 2y – 3 + y = 90°

⟹ 3y = 90° + 3

⟹ 3y = 93°

⟹ y = $\dfrac{\cancel{93}°}{\cancel{3}}$

⟹ y = 31°

Therefore,

• x = 2y – 3

⟹ x = 2(31) – 3

⟹ x = 62 – 3

⟹ x = 59°

Hence,

The measures of each angles are:

• x = 59°
• y = 31°

Answer 2

Answer: 51°and 31°.

Given:

$\sf Two\:angles\:are\:complementary.\\The\:larger\:angle\:is\:3^{\circ}\:less\:than\:twice\:the\:smaller\:angle.$

To find:

$\sf Measure\:of\:each\:angle.$

Explanation:

$\sf We\:know\:that,$

$\sf Complementary\:angles\:are\:those\:pair\:of\:angles\:whose\:sum\:is\:equal\:to\:90^{\circ}.$

$\sf Let\: x\:be\:the\:larger\:angle\:and\:y\:be\:the\:smaller\:angle.$

$\sf \therefore x+y=90^{\circ} \quad --(1)$

$\sf According\:to\:the\:question,$

$\sf x=2y-3$

$\sf Substituting\:the\:value\:of\:x\:in\:equation\:(1),\:we\:get:$

$\sf \Rightarrow (2y-3)+y=90$

$\sf \Rightarrow 2y+y-3=90$

$\sf \Rightarrow 3y=90-3$

$\sf \Rightarrow \boxed{\sf y=31^{\circ}}$

$\sf Putting\:the\:value\:of\:y\:in\:equation\:(1),we\:get:$

$\Rightarrow \sf x+31=90$

$\Rightarrow \sf x=90-31$

$\Rightarrow \boxed{\sf x=59^{\circ}}$

Therefore, the measure of the larger angle is 59° while the measure of the smaller angle is 31°.