Question

the supplementary angel of angel K is (12X+4)and the complement of angel K measure 6X what is K​

Answer 1

Given :

• Supplementary angle of K is (12X+4)
• Complementary angle of K is (6X)

To find : K

Information required :

• Supplementary angle are those angle whose sum is 180°.
• Complementary angle are those angle whose sum is 90°

Solution :

K & (12X +4) are supplementary,

➝ K + (12X + 4) = 180

➝ K + 12X = 180 - 4

➝ K + 12X = 176 ............ equation 1

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K & 6X are complementary

➝ K + 6X = 90

➝ 6X = 90 - K

➝ X = (90-K) ÷ 6........ Equation 2

On putting value of X from equation 2 into equation 1, we get;

$\sf \implies \: K \: + 12 \times \bigg( \dfrac{90 - K}{6} \bigg) = 176 \\ \\ \sf \implies \: K \: + \: 2(90 - K) = 176 \\ \\ \sf \implies \: K \: + \: 180 - \: 2K \: = \: 176 \\ \\ \sf \implies \: 180 - 176 = K \\ \\ \sf \implies \: K \: = 4$

ANSWER :

K = 4

Answer 2

Step-by-step explanation:

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$\text{\Large\underline{\red{Question:-}}}$

$\leadsto$ ● The supplementary angel of angel K is (12x + 4)and the complement of angel K measure 6x. What is K.

$\text{\Large\underline{\orange{To\ find:-}}}$

$\sf To\ find = \begin{cases} \sf{●\ In\ this\ question\ we\ have\ to\ find\ the\ value\ of\ K.} \end{cases}$

$\text{\Large\underline{\green{Given:-}}}$

$\frak Given = \begin{cases} \sf\pink{●\ Supplementary\ angle\ of\ K\ is\ (12x\ +\ 4).} \\ \\ \sf\pink{●\ Complementary\ of\ K\ is\ 6(x).} \end{cases}$

$\text{\Large\underline{\purple{Solution:-}}}$

● K and (12x + 4) are supplementary,

● $\sf{K\ +\ (12x\ +\ 4)\ =\ 180}$

● $\sf{K\ +\ 12x\ =\ 180\ -\ 4}$

● $\sf\purple{K\ +\ 12x\ =\ 176}$..........(1).

Now:-

● K and 6x are complementary,

● $\sf{K\ +\ 6x\ =\ 90}$

● $\sf{6x\ =\ 90\ -\ K}$

● $\sf\purple{x\ =\ \dfrac{90-K}{6}}$..........(2).

Now, we put the value of x from equation (2) into equation (1):-

● $\sf{K\ +\ 12\ ×\ \bigg (\dfrac{90-K}{6} \bigg)\ =\ 176}$

● $\sf{K\ +\ 2(90\ -\ K)\ =\ 176}$

● $\sf{K\ +\ 180\ -\ 2K\ =\ 176}$

● $\sf{180\ -\ 176\ =\ K}$

● $\sf\purple{K\ =\ 4}$

Hence:-

● The value of K = 4.

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