Question

( a+30)° and ( 2a)° are the measure of supplementary angles what is the measure of each angle ? what is the measure angles of complementary angle of smaller angle​

Answer 1

Solution :-

Given ,

• Two angles are supplementary i.e. ( a + 30 )° & ( 2a )°

We need to find ,

• Measure of each angle = ?
• Measure of the complementary of smaller angle = ?

♦ Measure of each angle :-

As we know that , supplementary angles means , if sum of two angles equal to 180° , so they are called as supplementary angles .

So ,

=> (a + 30)° + ( 2a )° = 180°

=> (3a + 30)° = 180°

=> 3a = 180° - 30°

=> a = 150°/3

=> a = 50°

Now measure of each angle ,

• ( a + 30° ) = 50° + 30° = 80°
• ( 2a ) = 2 ( 50° ) = 100°

Hence,. the measure of each angles is , 80° & 100° .

♦ Complement of smaller angle :-

Here , smaller angle is 80° ( a + 30° ) . So , as we know that , complement angle means , if sum of two angles equal to 90° , then the angles are called as complement angles.

Let the , complement of the smaller angle be x

So ,

=> 80° + x° = 90°

=> x = 90° - 80°

=> x = 10°

Hence , the complement of the smaller angles is 10° .

Answer 2

$\Large{\underline{\underline{\textsf{\maltese\: {\red{Given :-}}}}}}$

☞ (a + 30)° and 2a° are supplement of each other.

$\Large{\underline{\underline{\textsf{\maltese\: {\red{To Find :-}}}}}}$

☞ Measure of (a + 30)° and 2a° = ?

☞ Complementary of smaller angle = ?

$\Large{\underline{\underline{\textsf{\maltese\: {\red{Concept Implemented :-}}}}}}$

» The sum of two supplementary angles is 180°.

» Complementary of any angle = 90° - Given angle.

» The sum of two complementary angles is 90°.

$\Large{\underline{\underline{\textsf{\maltese\: {\red{Solution :-}}}}}}$

⨳ (a + 30)° + 2a° = 180° [Supplementary angle]

⇒ a + 30° + 2a = 180°

⇒ 3a + 30° = 180°

⇒ 3a = 180° - 30°

⇒ 3a = 150°

⇒ a = $\sf \dfrac{150^\circ}{3}$

⇒ a = 50°

Now we find the measure of the both angles by putting the value of ‘a’ that we have obtained.

☯︎ (a + 30)°

= 50° + 30°

= 80°

☯︎ 2a°

= 2 × 50°

= 100°

∴ The measure of the angles are 80° and 100° respectively.

We find that 100° > 80° so 80° is the smaller angle so will find the complement of 80°.

⨳ Complementary of any angle = 90° - Given angle

⇒ Complementary of 80° = 90° - 80°

⇒ Complementary of 80° = 10°

∴ The measure of the complementary of the smaller angle is 10°