Answer:
54
Step-by-step explanation:
angle A+angle B+Angle C =180 degree [ angle sum property of a triangle]
36 +90 + angle B =180 degree
126 +angle B =180 degree
angle B= 180-126
54 degree
Ans
![\bf Step-by-step~explanation:](https://tex.z-dn.net/?f=%5Cbf%20Step-by-step~explanation%3A)
We are given that BA is perpendicular to BD, so that must mean that <em>m∠ABD </em>is a right angle, or 90º. This means: (8x - 10) + (4x + 52) = 90º, since both of the angles add up to become a right angle. We have to solve for x in order to find <em>m∠CBD.</em>
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<u>PART 1</u>
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Equation: (8x - 10) + (4x + 52) = 90
Let's add the like values together first.
![\bf 8x+4x=12x\\-10+52 = 42](https://tex.z-dn.net/?f=%5Cbf%208x%2B4x%3D12x%5C%5C-10%2B52%20%3D%2042)
![\bf 12x+42=90](https://tex.z-dn.net/?f=%5Cbf%2012x%2B42%3D90)
![\bf Step~2:](https://tex.z-dn.net/?f=%5Cbf%20Step~2%3A)
Let's subtract 42 from both sides of the equation to isolate the variable we are solving for, x. Our goal is to isolate it completely to get a value that is equal to x.
![\bf12x+42(-42)=90(=42)\\12x=48](https://tex.z-dn.net/?f=%5Cbf12x%2B42%28-42%29%3D90%28%3D42%29%5C%5C12x%3D48)
![\bf Step~3:](https://tex.z-dn.net/?f=%5Cbf%20Step~3%3A)
Divide both sides by 12 to get our final answer for x.
![\bf\frac{12x}{12} =x\\\\\frac{48}{12}= 4\\\\x=4](https://tex.z-dn.net/?f=%5Cbf%5Cfrac%7B12x%7D%7B12%7D%20%3Dx%5C%5C%5C%5C%5Cfrac%7B48%7D%7B12%7D%3D%204%5C%5C%5C%5Cx%3D4)
<u>PART 2</u>
<u></u>
Now that we have x, we simply plug it into our equation for <em>m∠CBD. </em>
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![\bf4x+52\\4(4)+52](https://tex.z-dn.net/?f=%5Cbf4x%2B52%5C%5C4%284%29%2B52)
![\bf Step~2:](https://tex.z-dn.net/?f=%5Cbf%20Step~2%3A)
Multiply 4 and add 52.
![\bf 4*4=16\\16+52=68](https://tex.z-dn.net/?f=%5Cbf%204%2A4%3D16%5C%5C16%2B52%3D68)
![\large\boxed{\bf Our~final~answer: mCBD=68}](https://tex.z-dn.net/?f=%5Clarge%5Cboxed%7B%5Cbf%20Our~final~answer%3A%20mCBD%3D68%7D)
![\bold{\huge{\green{\underline{ Solution}}}}](https://tex.z-dn.net/?f=%5Cbold%7B%5Chuge%7B%5Cgreen%7B%5Cunderline%7B%20Solution%7D%7D%7D%7D)
![\bold{\underline{ Given :- }}](https://tex.z-dn.net/?f=%5Cbold%7B%5Cunderline%7B%20Given%20%3A-%20%7D%7D)
- <u>We </u><u>have </u><u>given </u><u>a</u><u> </u><u>right</u><u> </u><u>angled </u><u>triangle </u><u>whose </u><u>values </u><u>are </u><u>m</u><u>, </u><u> </u><u>n </u><u>and </u><u>2</u><u> </u>
![\bold{\underline{ To \: Find :- }}](https://tex.z-dn.net/?f=%5Cbold%7B%5Cunderline%7B%20To%20%5C%3A%20Find%20%3A-%20%7D%7D)
- <u>We </u><u>have </u><u>to </u><u>find </u><u>the </u><u>value </u><u>of </u><u>m </u><u>and </u><u>n</u>
![\bold{\underline{ Let's \: Begin :- }}](https://tex.z-dn.net/?f=%5Cbold%7B%5Cunderline%7B%20Let%27s%20%5C%3A%20Begin%20%3A-%20%7D%7D)
<u>In </u><u>the </u><u>given </u><u>right </u><u>angled </u><u>triangle</u><u>, </u><u>we </u><u>have </u>
- Perpendicular height = n units
- Base = 2 units
- Hypotenuse = m units
<u>Now</u><u>, </u><u> </u><u>By </u><u>using </u><u>trigonometric </u><u>ratios </u>
![\bold{\pink{ Sin Φ = }}{\bold{\pink{\frac{Perpendicular }{Hypotenuse}}}}](https://tex.z-dn.net/?f=%5Cbold%7B%5Cpink%7B%20Sin%20%CE%A6%20%3D%20%7D%7D%7B%5Cbold%7B%5Cpink%7B%5Cfrac%7BPerpendicular%20%7D%7BHypotenuse%7D%7D%7D%7D)
![\bold{\red{ Cos Φ = }}{\bold{\red{\frac{Base}{Hypotenuse }}}}](https://tex.z-dn.net/?f=%5Cbold%7B%5Cred%7B%20Cos%20%CE%A6%20%3D%20%7D%7D%7B%5Cbold%7B%5Cred%7B%5Cfrac%7BBase%7D%7BHypotenuse%20%7D%7D%7D%7D)
![\bold{\blue { tan Φ = }}{\bold{\blue{\frac{Perpendicular }{Base }}}}](https://tex.z-dn.net/?f=%5Cbold%7B%5Cblue%20%7B%20tan%20%CE%A6%20%3D%20%7D%7D%7B%5Cbold%7B%5Cblue%7B%5Cfrac%7BPerpendicular%20%7D%7BBase%20%7D%7D%7D%7D)
<u>According </u><u>to </u><u>the </u><u>question </u><u>:</u><u>-</u>
![\bold{ Cos \: 45° = }{\bold{\frac{2}{m}}}](https://tex.z-dn.net/?f=%5Cbold%7B%20Cos%20%5C%3A%2045%C2%B0%20%3D%20%7D%7B%5Cbold%7B%5Cfrac%7B2%7D%7Bm%7D%7D%7D)
![\bold{ 1/√2= }{\bold{\frac{2}{m}}}](https://tex.z-dn.net/?f=%5Cbold%7B%201%2F%E2%88%9A2%3D%20%7D%7B%5Cbold%7B%5Cfrac%7B2%7D%7Bm%7D%7D%7D)
![\bold{\red{ m = 2√2 \: units }}](https://tex.z-dn.net/?f=%5Cbold%7B%5Cred%7B%20m%20%3D%202%E2%88%9A2%20%5C%3A%20units%20%7D%7D)
- <u>We </u><u>know </u><u>that </u><u>,</u><u> </u><u>Sum </u><u>of </u><u>Angles</u><u> </u><u>of </u><u>triangle </u><u>is </u><u>1</u><u>8</u><u>0</u><u>°</u><u> </u><u>.</u>
<u>Therefore</u><u>, </u>
Let the unknown angle be x
![\sf{ 45° + x + 90° = 180° }](https://tex.z-dn.net/?f=%5Csf%7B%2045%C2%B0%20%2B%20x%20%2B%2090%C2%B0%20%3D%20180%C2%B0%20%7D)
![\sf{ x = 180° - 135 ° }](https://tex.z-dn.net/?f=%5Csf%7B%20x%20%3D%20180%C2%B0%20-%20135%20%C2%B0%20%20%7D)
![\sf{ x = 45° }](https://tex.z-dn.net/?f=%5Csf%7B%20x%20%3D%2045%C2%B0%20%20%20%7D)
<u>Now</u><u>, </u>
![\bold{ Cos \: x° = }{\bold{\frac{n}{2√2}}}](https://tex.z-dn.net/?f=%5Cbold%7B%20Cos%20%5C%3A%20x%C2%B0%20%3D%20%7D%7B%5Cbold%7B%5Cfrac%7Bn%7D%7B2%E2%88%9A2%7D%7D%7D)
![\bold{ Cos \: 45° = }{\bold{\frac{n}{2√2}}}](https://tex.z-dn.net/?f=%5Cbold%7B%20Cos%20%5C%3A%2045%C2%B0%20%3D%20%7D%7B%5Cbold%7B%5Cfrac%7Bn%7D%7B2%E2%88%9A2%7D%7D%7D)
![\bold{ 1/√2= }{\bold{\frac{n}{2√2}}}](https://tex.z-dn.net/?f=%5Cbold%7B%201%2F%E2%88%9A2%3D%20%7D%7B%5Cbold%7B%5Cfrac%7Bn%7D%7B2%E2%88%9A2%7D%7D%7D)
![\bold { n = 2√2/√2 }](https://tex.z-dn.net/?f=%5Cbold%20%7B%20n%20%3D%202%E2%88%9A2%2F%E2%88%9A2%20%20%7D)
![\bold{\red{ n = 2\: units }}](https://tex.z-dn.net/?f=%5Cbold%7B%5Cred%7B%20n%20%3D%202%5C%3A%20units%20%7D%7D)
Thus, The value of m = 2√2 and n = 2
![\sf{\blue{ Hence, \: option \: D \: is \: Correct }}](https://tex.z-dn.net/?f=%5Csf%7B%5Cblue%7B%20Hence%2C%20%5C%3A%20option%20%5C%3A%20D%20%5C%3A%20is%20%5C%3A%20Correct%20%7D%7D)
A.) 18 m
lets say u star at point A (0m from the start) it then moves to point B (20m from the start (20x1=20)) then it moves to point C (2m back from B making it 18m from A (.5x4=2))