Can you find the value of X+Y? | (Cyclic Quadrilateral) |

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Learn how to solve for angles X+Y. Important Geometry and Algebra skills are also explained: Cyclic Quadrilateral; angle sum. Step-by-step tutorial by PreMath.com
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Комментарии : 29

@georgebliss964 9 часов назад

Opposite angles adding up to 180 degrees. (5y - 3) + (9x + 2) = 180..........(1) Also, 5y + (8x + 3) = 180.........(2) Subtracting (2) from (1). (5y - 3) + (9x + 2) - 5y - (8x + 3) = 0. 5y - 3 + 9x + 2 - 5y - 8x - 3 = 0. x - 4 = 0. x = 4. Substituting in (2). 5y + 35 = 180. 5y = 145. y = 29. x + y = 4 + 29 = 33.

@scottdort7197 9 часов назад

You only needed two equations. You didn’t need equation 3. Two equations and two unknowns will get you the solution. No need to do extra work.

@joeschmo622 9 часов назад

I would do that, too, if only to "check my work". 🧠

@rey-dq3nx 8 часов назад

Do you think a tenured math professor doesn’t know that?

@sergioaiex3966 7 часов назад

Obviously two equations and two unknowns are needed, however, I think Mister wanted to detail another resource for the solution

@imetroangola4943 3 часа назад

Você tem toda razão!!!

@imetroangola4943 3 часа назад

@@joeschmo622 não sei se ele é professor de matemática, pois professor com a matemática apurada não faz isso!

@AmirgabYT2185 7 часов назад

8x+3+5y=180° 5y-3+9x+2=180° 8x+3+5y=5y-3+9x+2 -x=-4 x=4 y=29 x+y=4+29=33 Answer: 33

@prossvay8744 8 часов назад

9x+5y-3+2=180 9x+5y=181 (1) 8x+5y+3=180 8x+5y=177 (2) (1)&(2) 9x-8x=181-177=4 So x=4° 9(4)+5y=181 5y=181-36=145 So y=45° So x+y=4+29=33°.❤❤❤

@Birol731 6 часов назад

My way of solution ▶ The sum of the opposite interior angles of a Cyclic Quadrilateral is 180°, therefore: ∠ADC + ∠CBA= 180° 8x+3+5y= 180° 8x+5y= 177° ∠BAD + ∠DCB= 180° 5y-3+9x+2= 180° 5y+9x= 181° ⇒ 5y+8x= 177° 5y+9x= 181° ⇒ 5y+9x= 181° -5y-8x= -177° ⇒ x= 4° y= (181°-9*4°)/5 y= 29° x+y= 4°+29° x+y= 33° is the answer !

@Birol731 6 часов назад

Another way of solution ▶ ∠ ADC is the half of the circle segment ∠CA ∠CA= 2* ∠ ADC ∠CA= 2* (8x+3) ∠CA= 16x+6 ∠CBA is the half of the circle segment ∠AC ∠AC= 2* ∠CBA ∠AC= 2*5y ∠AC= 10y ⇒ the sum of the both circle segments is equal to 360° ∠CA+ ∠AC = 360° 16x+6 + 10y= 360° by dividing both sides of 2, we get: 8x+3+5y= 180° 8x+5y= 177° b) ∠BAD is the half of the circle segment ∠DB ∠DB= 2* ∠BAD ∠DB= 2*(5y-3) ∠DB= 10y-6 ∠DCB is the half of the circle segment ∠BD ∠BD= 2* ∠DCB ∠BD= 2*(9x+2) ∠BD= 18x+4 ⇒ the sum of the both circle segments is equal to 360° ∠DB+ ∠BD = 360° 10y-6+18x+4= 360° 10y+18x-2= 360° by dividing both sides of 2, we get: 5y+9x-1= 180° 5y+9x= 181° ⇒ 5y+8x= 177° 5y+9x= 181° ⇒ x= 4° y= (181°-9*4°)/5 y= 29° x+y= 4°+29° x+y= 33°

@marioalb9726 6 часов назад

5y - 3° + 9x+ 2° = 8x+ 3° + 5y = 180° x = 4° 5y = 180° - 3° - 8x = 177°-8x y = 29° x+y = 33° ( Solved √ ) Where are those who everytime write "units" or " square units" ??? instead a recognized standard unit. Those who claim when we write "cm" or any unit of the international units system Why don't you write "units" now, in your comments ??? or "angle units" ??? if you pay attention, the statement of this exercise DOESN'T mention that are degrees , and in that case, the given data would be wrong !!

@marioalb9726 6 часов назад

5y - 3 + 9x+ 2 = 8x+ 3 + 5y x = 4 radians 8x+ 3 + 5y = π 5y = π - 3 - 8x = 0,141592 -8x y = -6,37 radians, IMPOSIBLE !!! This exercise just works with sexagesimal degrees, and was not set in the input data !!! Where are those that everythime writes "units" ?? instead a recognized standard unit !!!

@MrPaulc222 2 часа назад

I had to look up the properties of a CQ first as it's been a while. It looks like x = 4 and y = 29, but I stand to be corrected. edit; Nearly forgot to answer the question LOL. x+y = 33

@sergioaiex3966 7 часов назад

Solution: It's a Cyclic Quadrilateral, therefore, the opposite interior angles must add up to 180° (9x + 2) + (5y - 3) = 180° (8x + 3) + 5y = 180° 9x + 2 + 5y - 3 = 180° 9x + 5y = 181° ... ¹ 8x + 3 + 5y = 180° 8x + 5y = 177° ... ² ¹ - ² x = 4 8 (4) + 5y = 177° 32 + 5y = 177 5y = 177 - 32 y = 145/5 y = 29 x + y = 4 + 29 x + y = 33

@unknownidentity2846 8 часов назад

Let's face this challenge: . .. ... .... ..... A convex quadrilateral ABCD is cyclic if and only if its opposite angles add up to 180°: ∠BAD + ∠DCB = ∠CBA + ∠ADC = 180° (5y − 3°) + (9x + 2°) = (5y) + (8x + 3°) 5y − 3° + 9x + 2° = 5y + 8x + 3° ⇒ x = 4° 5y − 3° + 9x + 2° = 180° 5y + 9x = 181° 5y + 9*4° = 181° 5y + 36° = 181° 5y = 145° ⇒ y = 29° 5y + 8x + 3° = 180° 5y + 8x = 177° 5y + 8*4° = 177° 5y + 32° = 177° 5y = 145° ⇒ y = 29° ✓ Now we are able to solve this problem: x + y = 4° + 29° = 33° Best regards from Germany

@yalchingedikgedik8007 32 минуты назад

Very nice Good job Thanks Sir With my respects ❤❤❤❤❤❤

@wackojacko3962 5 часов назад

I love this problem because I have the guilty pleasure of falling down the Rabbit hole to the orthocenter too meet the Grand Poobah of Rabbits. 🙂

@ยี่สิบเก้าพฤศจิกา 6 часов назад

ไม่จำเป็นต้องเอา(-2)× แต่ให้เอา (1)-(2)จะได้9X+5Y-8X-5Y=181-177 ; X=4

@ericwickeywoodworkersurfbo6135 6 часов назад

Awesome video! Is it arbitrary which equations you add up? Or is the only reason for picking any two is that the arithmetic is clearer and easier for them?