Calculate angle X in a 5-sided irregular Polygon | Learn how to Solve this Geometry problem Quickly

Learn how to find the angle X in the given diagram. 5-sided irregular Polygon. Solve this tricky geometry problem by using interior angle sum formula.

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Calculate angle X in a 5-sided irregular Polygon | Learn how to Solve this Geometry problem Quickly

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#PythagoreanTheorem #Pythagorean #ParallelLines
#HowtoCalculatethedistance #Findthedistanceofthelinesegment #LineSegment #length #distance #blackpenredpen #ComplementaryAngles #OlympiadMathematics
#FindtheAngleX #HowtoSolvethisTrickyGeometryProblemQuickly #IsoscelesTriangleProperty
#IsoscelesTriangle #IsoscelesTriangles #Isosceles #Triangle #Triangles
#CorrespondingAngles #ExteriorAngleTheorem #AlternateInteriorAngles #CyclicQuadrilateral

Olympiad Mathematics
pre math
Po Shen Loh
Learn how to find the angle X
Alternate interior angles
Vertical Angles
exterior angle theorem
Exterior Angles
premath
premaths
irregular Polygon
Polygon
5-sided irregular Polygon
5-sided Polygon
Interior Angle Sum

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[banja]

If you don't remember the formula for the inner angle of a polygon, think of how many triangles you can exactly fit into it. In this case 3, so it's 180*3.

[풍천-ih]

오각형이 540도인 것을 몰라서 사각형을 덧그려서 풀어보았다.
360-52-86-144=78
180-78=102
360-102=258÷2=129

[rosoltalosig]

There are two unknowns angle (x), how do you know they are the same or equal angles?

[thomasalvis]

I took a different approach, extending the sides with angle x to make a quadrilateral.

[telosfd]

I did not knew this mathematical formula! Why are these two angles X equal?

[FrankieIymon]

Great!! You made it easily understandable my teacher made it lol hard😅

[yalchingedikgedik]

Thanks PreMath
Very nice and useful .
Good luck

[vincentxie]

2:20 I kinda didn't understand when he put the 2x in the equation

[RjPoge-et]

How do you get the 258⁰? I don't understand the last one

[PravinPatel-mlvq]

My opinion is not correct -You assumed two remaining angle are equal

[santiagoarosam]

Another way to solve it.- We can transform the pentagon of the proposed scheme into a quadrilateral by prolonging the left side of the 52º angle and the lower side of the 144º angle until their intersection in the new vertex “B”, which together with the deleted vertices determines an isosceles triangle with angles ∠B, ∠(180-X) and ∠(180-X) → ∠B=180º - 2(180º - X) → ∠B=2X – 180º →→ In the constructed quadrilateral, the sum of internal angles is 360º → 52º+86º+144º+B = 360º → ∠B=78º →→ 78º = 2X – 180º → X=(78º+180º)/2= 129º → ∠X=129º
Regards

[massimogranzotto]

Complimenti professore con spiegazioni fatte così bene mi fa appassionare alla geometria.
Grazie ancora

[theoyanto]

Ah...you gave us an easy one thanks, made me feel real clever :)

[seroujghazarian]

2x+144+86+52=540
x+72+43+26=270
x+141=270
x=129°