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3241004551 [841]
3 years ago
5

The measure of an angle is 135 degrees. What is the measure of its supplementary angle ?

Mathematics
1 answer:
Marat540 [252]3 years ago
6 0

Remember that if two angles are supplementary, then the sum of their measures is 180°. So if the measure of an angle is 135 degrees. What is the measure of its supplement?

If the measure of an angle is 135°,

then the measure of its supplement is 45°.

We can find the measure of its supplement by taking 180 minus the measure of the original angle which in this case is 180 - 135 or 45°.

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Let T be the total number of points required to advance.

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T=a+c+d+3b\\3b=T-a-c-d\\b=\frac{T-a-c-d}{3}

They need to score (T - a - c - d)/3, in the district match in order to win.

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Check the picture below.

\bf \stackrel{\measuredangle DAC}{4y+2x}~~=~~\stackrel{\measuredangle BCA}{9y-x}\implies 2x=5y-x\implies 3x=5y\implies \boxed{x=\cfrac{5y}{3}} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\measuredangle DAB}{[(4y+2x)+35]}~~+~~\stackrel{\measuredangle ADC}{5x+4}~~=~~180\implies 4y+2x+5x+39 = 180 \\\\\\ 4y+7x+39=180\implies 4y+7x=141\implies \stackrel{\textit{substituting "x"}}{4y+7\left( \boxed{\cfrac{5y}{3}} \right)} = 141

\bf 4y+\cfrac{35y}{3}=141\implies \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{3}}{3\left( 4y+\cfrac{35y}{3} \right)=3(141)}\implies 12y+35y=423 \\\\\\ 47y=423\implies y=\cfrac{423}{47}\implies \blacktriangleright y = 9 \blacktriangleleft \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{since we know that}}{x=\cfrac{5y}{3}}\implies x = \cfrac{5(9)}{3}\implies \blacktriangleright x = 15 \blacktriangleleft

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