1. Find x if 6x and 3x are (a) Complementary angles (b) supplementary

1.	1. Find x if 6x and 3x are (a) Complementary angles (b) supplementary angles
Answer» Answer: a) 10° b) 20° Step-by-step explanation: As per the provided information in the given question, we have : 6x and 3x are complimentary angles. (Case 1) 6x and 3x are supplementary angles. (Case 2) We are asked to calculate the value of x in both cases. $\underline{ \bf{ \maltese \; \; \; Case \: 1 \: : \; \; \; }}$ If the sum of TWO angles is 90°, then they are CALLED complimentary angles to each other. Here, 6x and 3x are two angles are complimentary angles, so their sum will be 90°. $\longrightarrow \sf{\quad { 6x + 3x = 90^\circ}} \\$ Performing addition of the TERMS in LHS. $\longrightarrow \sf{\quad { 9x = 90^\circ}} \\$ Transposing 9 from LHS to RHS, its arithmetic operator will get changed. $\longrightarrow \sf{\quad { x = \cancel{\dfrac{90^\circ}{9}} }} \\$ Dividing 90° by 9. $\longrightarrow \quad\underline{\boxed { \textbf{\textsf{ x = 10}}^\circ}} \\$ The value of x if 6x and 3x are complimentary angles is 10°. $\underline{ \qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad} \\$ $\underline{ \bf{ \maltese \; \; \; Case \: 2 \: : \; \; \; }}$ If the sum of two angles is 180°, then they are called supplementary angles to each other. Here, 6x and 3x are two angles are supplementary angles, so their sum will be 180°. $\longrightarrow \sf{\quad { 6x + 3x = 180^\circ}} \\$ Performing addition of the terms in LHS. $\longrightarrow \sf{\quad { 9x = 180^\circ}} \\$ Transposing 9 from LHS to RHS, its arithmetic operator will get changed. $\longrightarrow \sf{\quad { x = \cancel{\dfrac{180^\circ}{9}} }} \\$ Dividing 180° by 9. $\longrightarrow \quad\underline{\boxed { \textbf{\textsf{ x = 20}}^\circ}} \\$ The value of x if 6x and 3x are supplementary angles is 20°.

1. Find x if 6x and 3x are (a) Complementary angles (b) supplementary angles

Answer»

Answer:

a) 10°

b) 20°

Step-by-step explanation:

As per the provided information in the given question, we have :

6x and 3x are complimentary angles. (Case 1)
6x and 3x are supplementary angles. (Case 2)

We are asked to calculate the value of x in both cases.

$\underline{ \bf{ \maltese \; \; \; Case \: 1 \: : \; \; \; }}$

If the sum of TWO angles is 90°, then they are CALLED complimentary angles to each other. Here, 6x and 3x are two angles are complimentary angles, so their sum will be 90°.

$\longrightarrow \sf{\quad { 6x + 3x = 90^\circ}} \\$

Performing addition of the TERMS in LHS.

$\longrightarrow \sf{\quad { 9x = 90^\circ}} \\$

Transposing 9 from LHS to RHS, its arithmetic operator will get changed.

$\longrightarrow \sf{\quad { x = \cancel{\dfrac{90^\circ}{9}} }} \\$

Dividing 90° by 9.

$\longrightarrow \quad\underline{\boxed { \textbf{\textsf{ x = 10}}^\circ}} \\$

The value of x if 6x and 3x are complimentary angles is 10°.

$\underline{ \qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad} \\$

$\underline{ \bf{ \maltese \; \; \; Case \: 2 \: : \; \; \; }}$

If the sum of two angles is 180°, then they are called supplementary angles to each other. Here, 6x and 3x are two angles are supplementary angles, so their sum will be 180°.

$\longrightarrow \sf{\quad { 6x + 3x = 180^\circ}} \\$