Question

If two adjacent angle of a rhombus are (5×-5) and (10×+35), then the value of x?

Answer 1

$\bold{Given : }$

If two adjacent angle of a rhombus are (5×-5) and (10×+35).

$\bold{To \: find \: out : }$

Find the value of x ?

$\bold{Solution : }$

• One angle = 5x - 5

• Another angle = 10x + 35

We know that,

Sum of adjacent angle of a rhombus = 180°

$: \implies(5x - 5) + (10x + 35) = 180 \degree$

$: \implies15x + 30 = 180 \degree$

$: \implies15x = 180 \degree - 30 \degree$

$: \implies15x = 150 \degree$

$: \implies \: x = \cancel \frac{150}{15}$

$: \implies x = 10 \degree$

Hence, the value of x is 10° .

Answer 2

⠀⠀⠀$\huge\underline{ \mathrm{ \red{QueS{\pink{tiOn}}}}}$

If two adjacent angle of a rhombus are (5×-5) and (10×+35), then the value of x?

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⠀⠀⠀$\huge{ \underline{ \purple{ \bold{ \underline{ \mathrm{ExPlanA{\green{TiOn }}}}}}}}$

$\bf{ \pink{{GivEn}\begin{cases}\textsf{two \: adjacent \: angles \: are \: given}\\\textsf{one \: angle \: is \: (10 x+35) }\\\textsf{other \: angle \: is \: (5x - 5)}\end{cases}}}$

$\large\underline{ \underline{ \red{ \bold {To \:Find}}}}$

$\bf\:\green{we\:need\:to\:find\:the\:value\:of\:x}$

⠀⠀⠀⠀⠀$\huge\underline{ \underline{ \orange{ \bold{sOluTiOn}}}}$

⠀⠀⠀⠀⠀

$\bf\:\blue{sum\:of\:two\: adjacent\: angles= 180°}$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀so,

➩⠀⠀⠀⠀⠀$\bf\:(5x-5)+(10x+35)=180$

➩⠀⠀⠀⠀⠀$\bf\:5x-5+10x+35=180$

➩⠀⠀⠀⠀⠀$\bf\:15x+30=180$

➩⠀⠀⠀⠀⠀$\bf\:15x=180-30$

➩⠀⠀⠀⠀⠀$\bf\:15x=150$

➩⠀⠀⠀⠀⠀$\bf \: x = \cancel\dfrac{150}{15}$

➩⠀⠀⠀$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \huge\underline {\boxed{ \red{x = 10}}}$

⠀⠀⠀⠀⠀⠀⠀⠀so,

• first Angles =( 5 x - 5 )

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀= 5 × 10 -5

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀= 50-5

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀=$\large\underline {\boxed{ \orange{\:\:\: 45°\:\:\:}}}$

• Second angle = (10 x - 35)

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀= 10×10-35

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀=100-35

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀=$\large\underline {\boxed{ \orange{ \:\:\:65°\:\:\:}}}$

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