9.
<2 and <6 are right angles by the definition of perpendicular lines.
Since corresponding angles are congruent, m || n.
11.
In a triangle, the measures of the three angles add to 180 degrees.
If one angle is a right angle, then that angle measures 90 degrees. The other two angle measures plus 90 degrees add to 180 degrees, so the other two angle measures add to 90 degrees. In a right triangle there is a right angle and two other angles that are complementary.
Now look at your problem.
One angle is a right angle.
The other two angles are complementary, so their measures add to 90 deg.
8x + 2 + 9x + 3 = 90
17x + 5 = 90
17x = 85
x = 5
<em>Given, 9−7x=5−3x</em>
<em>Given, 9−7x=5−3xPut x terms on one side and constants on another side.</em>
<em>Given, 9−7x=5−3xPut x terms on one side and constants on another side.⇒9−5=7x−3x</em>
<em>Given, 9−7x=5−3xPut x terms on one side and constants on another side.⇒9−5=7x−3x⇒4=4x</em>
<em>Given, 9−7x=5−3xPut x terms on one side and constants on another side.⇒9−5=7x−3x⇒4=4x⇒x= </em><em>4</em><em>/</em><em>4</em><em> </em><em> =1</em>
<em> =1Hence, required solution is x=1.</em>
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<h2>
Explanation:</h2>
The nth term of an arithmetic series (
) and the sum of an arithmetic series (Sum), for n terms, can be found as:
![a_{n}=a_{1}+d(n-1) \\ \\ Sum=\frac{n}{2}[2a_{1}+(n-1)d] \\ \\ \\ Where: \\ \\ a_{1}:First \ term \\ \\ d:Common \ difference \\ \\ n=Number \ of \ term](https://tex.z-dn.net/?f=a_%7Bn%7D%3Da_%7B1%7D%2Bd%28n-1%29%20%5C%5C%20%5C%5C%20Sum%3D%5Cfrac%7Bn%7D%7B2%7D%5B2a_%7B1%7D%2B%28n-1%29d%5D%20%5C%5C%20%5C%5C%20%5C%5C%20Where%3A%20%5C%5C%20%5C%5C%20a_%7B1%7D%3AFirst%20%5C%20term%20%5C%5C%20%5C%5C%20d%3ACommon%20%5C%20difference%20%5C%5C%20%5C%5C%20n%3DNumber%20%5C%20of%20%5C%20term)
So, in this exercise:
![a_{1}=a=9 \\ \\ d=4 \\ \\ n=16 \\ \\ \\ Sum=\frac{16}{2}[2(9)+(16-1)4] \\ \\ Sum=8[18+(15)4] \\ \\ Sum=8[18+60] \\ \\ Sum=8[78] \\ \\ \boxed{Sum=624}](https://tex.z-dn.net/?f=a_%7B1%7D%3Da%3D9%20%5C%5C%20%5C%5C%20d%3D4%20%5C%5C%20%5C%5C%20n%3D16%20%5C%5C%20%5C%5C%20%5C%5C%20Sum%3D%5Cfrac%7B16%7D%7B2%7D%5B2%289%29%2B%2816-1%294%5D%20%5C%5C%20%5C%5C%20Sum%3D8%5B18%2B%2815%294%5D%20%20%5C%5C%20%5C%5C%20Sum%3D8%5B18%2B60%5D%20%5C%5C%20%5C%5C%20Sum%3D8%5B78%5D%20%5C%5C%20%5C%5C%20%5Cboxed%7BSum%3D624%7D)
<h2>Learn more:</h2>
Missing numbers in triomino: brainly.com/question/10510270
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