ZA and B are supplementary angles. If m A = (7x +3) and m ZB = (7x +23)", then find the measure of ZA.

Mathematics

1 answer:

Anna71 [15]3 years ago

4 0

Answer:

Angle A measures 80º.

Step-by-step explanation:

Supplementary angles:

Two angles are called supplementary when their measures add to 180º.

In this question:

Angle A measures 7x + 3

Angle B measures 7x + 23

Since they are supplementary:

$A + B = 180$

$7x + 3 + 7x + 23 = 180$

$14x + 26 = 180$

$14x = 154$

$x = \frac{154}{14}$

$x = 11$

Measure of Angle A:

Since x = 11

7*11 + 3 = 77 + 3 = 80º

Angle A measures 80º.

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ikadub [295]

so first off, let's simplify both equations, starting off by multiplying both sides by the LCD of all fractions, to do away with the denominators.

$\bf \cfrac{10(x-y)-4(1-x)}{3}=y\implies \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{3}}{10(x-y)-4(1-x)=3y} \\\\\\ 10x-10y-4+4x=3y\implies \boxed{14x-13y=4} \\\\[-0.35em] ~\dotfill\\\\ 7+x-\cfrac{x-3y}{4}=2x-\cfrac{y+5}{3}\implies \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{12}}{12\left( 7+x-\cfrac{x-3y}{4} \right)=12\left( 2x-\cfrac{y+5}{3} \right)} \\\\\\ 84+12x-3(x-3y)=24x-4(y+5) \\\\\\ 84+12x-3x+9y=24x-4y-20\implies \boxed{-15x+13y=-124}$

now, let's do some elimination on those two simplified equations.

$\bf \begin{array}{cllcl} 14x&-13y&=&4\\ -15x&+13y&=&-124\\\cline{1-4} -x&&=&-120 \end{array}~\hfill x=\cfrac{-120}{-1}\implies \blacktriangleright x=120 \blacktriangleleft \\\\\\ \stackrel{\textit{substituting on the 1st equation}}{14(120)-13y=4}\implies 1680-13y=4\implies 1680-4=13y \\\\\\ 1676=13y\implies \blacktriangleright \cfrac{1676}{13}=y \blacktriangleleft \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill \left( 120~,~\frac{1676}{13} \right)~\hfill$

6 0

3 years ago

What is the angle measure of an arc bounding sector with an area of 5pie square miles?

Snowcat [4.5K]

if the diameter is 20, the its radius must be half that or 10.

$\textit{area of a sector of a circle}\\\\ A=\cfrac{\theta \pi r^2}{360}~~ \begin{cases} r=radius\\ \theta =\stackrel{degrees}{angle}\\[-0.5em] \hrulefill\\ A=5\pi \\ r=10 \end{cases}\implies \begin{array}{llll} 5\pi =\cfrac{\theta \pi (10)^2}{360}\implies 5\pi =\cfrac{5\pi \theta }{18} \\\\\\ \cfrac{5\pi }{5\pi }=\cfrac{\theta }{18}\implies 1=\cfrac{\theta }{18}\implies 18=\theta \end{array}$