Find angle X | Learn how to Solve this Geometry problem Quickly

Learn how to find the angle X in the given diagram. Solve this tricky geometry problem by using Vertical angles and Exterior angles Theorems.

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Find angle X | Learn how to Solve this Geometry problem Quickly

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Learn how to find the angle X
Alternate interior angles
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Exterior Angles
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[spiritualandangelicencounters]

For me I just quickly seen and calculated in my head that the first angle extends past 90* by 41* and the second angle extends past 90* by 13* so I just simply added 41+13=54
I did enjoy all the calculations you made though this was fun thanks 😊

[sumanmukherjee]

This was a good question.. But we can solve it also by exterior angle theorem because when we got one angle is x and other is 49 degree inside the traingle and the angle out of the traingle is 103 degree then we can write x+49 =103 or x=54 degree

[Reddogovereasy]

You are an excellent instructor. Thought we hear the theorem repeated in each video and in each lesson, I deeply appreciate your doing so. Thank you for your desire to teach and teach well.

[divyanshujain]

Love from India 🇮🇳 ♥. I solved the puzzle in mind.

[massimogranzotto]

Con le sue spiegazioni anche la geometra inizio a capirla
Grazie professore

[aaronbredon]

I just did 131+103-180 to get the amount the 2 angles exceeded the 180 degrees of a straight line. This gives the overlap angle, which is x. You can verify by constructing a parallel horizontal line through the intersection of the 2 lines. Then the 2 angles overlap by x degrees.

[dcorman]

You just need to move up the horizontal line a notch higher, at the Apex of the angle X…

… then the formula/solution is X = 131 + 103 - 180 = 54 😊

[thomasgreene]

You can also just construct two perpendiculars to the horizontal line segments passing through the vertices of the defined angles and a third line parallel to the perpendiculars and passing through the vertex of the anglle x.. The angle x is then the sum of the angles between the first two perpendiculars and the intersecting line segments (131-90 =41; 103-90 = 13; x = 41+13 = 54).

[Paul-sjdb]

Another way to solve this is to manipulate the image. Move the top line down so it is inline with the bottom parallel line. Then slide it to the right until the corner lines up with the corner on the parallel line.

At this point you can see that X is the overlap between the two angles. So, X is the sum of the two angles minus 180.

You can prove this algebraically by replacing the two angles with A and B and following the logic in this video and then simplifying.

[chrisk.]

So easy, my aughter 12 years old were able to solve this in 5 min.
There is one condition both bases of the angles should parallel on this example isn't so perfect drawn.

[kennethstevenson]

Good way to check knowledge of angle measure of a diagram with parallel lines, Draw the figure, extend lines past the point of intersection and begin marking alternate interior angles, vertical angles, angles that total 180 degrees, angles that total 360 degrees until you reach angle X which is 54 degrees. You can quickly find the measure of every angle in the resulting diagram.

[guyhoghton]

Mentally slide (without rotation) one of the given angles so that its vertex coincides with the vertex of the other given angle. In doing so, the vertex of angle X will slide down to coincide with the other two vertices. Now the two given angles 131° and 103° form a straight line of 180° but they overlap by the angle X. Therefore find the value of X by subtracting 180° from their sum.

[kalyanbasak]

🙏🏼 proffessor sir, excellent teaching capacity, 103-49=54°may be shared as an answer sir

[theoyanto]

That was quite easy, but still good practice

[mathejogi]

If we move both angles to the intersection point, they will "overlap" for 54 degrees, that means there sum is 54 degrees more than 180 degrees

[nityasindhu]

Easy question, great going.. Bring more questions of exponents and its simplification..

[telosfd]

At 4:04 minutes we transfer (+126) to the second part of the equation with the sign changed, as (-126). The fact that we divide both parts by (-126) seems wrong since in the first part we have (X+126) and not multiplication. Αm I wrong;

[jimmcfarland]

Even easier. Add the two angles and subtract 180.

[rjones]

There is a quicker and easier way. Bring the LHS angle down to join up with the RHS angle forming a "V", so we have 131 + 103 = 234 - 180 = 54

[AnonimityAssured]

An easy mental calculation, but an interesting problem. The calculation can be reduced to an addition and a subtraction.

(Spoiler alert.)

131° + 103° − 180° = 54°.