∠ABD and ∠BDE are supplementary. Find the measures of both angles.

Mathematics

1 answer:

Gnom [1K]4 years ago

5 0

Supplementary means that the angles have to add up to 180, so you have your equation.

180=5x+17x-18

198=22x

x=9

Then to find the measures of the angles, you plug x back in.

m∠ABD=5(9)=45 degrees

m∠BDE=17(9)-18=153-18=135 degrees

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Pavel [41]

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( $\partial E$ denotes the boundary of $E$ ), we want to find $M(x,y)$ and $L(x,y)$ such that

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$\begin{cases}M(x,y)=\dfrac x2\\\\L(x,y)=-\dfrac y2\end{cases}\implies\begin{cases}\dfrac{\partial M}{\partial x}=\dfrac12\\\\\dfrac{\partial L}{\partial y}=-\dfrac12\end{cases}\implies\dfrac{\partial M}{\partial x}-\dfrac{\partial L}{\partial y}=1$

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$\displaystyle\frac12\int_0^{2\pi}(-17\sin t(-5\sin t)+5\cos t(17\cos t))\,\mathrm dt$

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Notice that $x^{2/3}+y^{2/3}=4^{2/3}$ kind of resembles the equation for a circle with radius 4, $x^2+y^2=4^2$ . We can change coordinates to what you might call "pseudo-polar":