Calculate the angle X and justify | Learn how to Solve the Geometry problem Quickly

Learn how to find the angle X in the given diagram. Solve this tricky geometry problem by using the isosceles triangle properties and Exterior Angle Theorem.

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Calculate the angle X and justify | Learn how to Solve the Geometry problem Quickly

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Olympiad Mathematics
pre math
Po Shen Loh
Learn how to find the angle X
Isosceles Triangles
Triangle
premath
premaths
Exterior Angle Theorem

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[alexniklas]

<CAD= 180- 147= 33°
<ADC= 147- a; <ADC= 180-2a
147- a= 180- 2a; 2a- a= 180- 147;
a= 33°
<ACB= 180- 33- 66= 81°
<x= 180- 81= 99°

[DR-kzli]

Your lessons are always very clear. I compared the same exercise solved by you and other profs on the web. Your method is the best. At school ( a long time ago! ) I had very good profs of math and your lessons remember me that time. Thanks a lot.

[Waldlaeufer]

Let's have a look at 147°. So, we have 33° to accomplish 180° inside the left triangle.
Let's look at the isosceles triangle on the right. The bottom corners are both 2α. 2α is the exterior angle of the left triangle and, therefore, 2α = α + 33°. So, α must be 33° as well.
x is the exterior angle of the whole triangle. So x must be equal to the opposite interior angles 33° and 2α. So, x = 33° + 2α = 33° + 66° = 99°.

[vidyadharjoshi]

Angle X = 180 - ( 180 - 4a + a ) = 3a
Angle CAD= 180 - 147 = 33; Angle CDA = 180 - 2a. Angles ( CAD + CDA + a ) = 180.
So 33 + 180 - 2a + a = 180 ; 33 - a = 0 So a = 33 so X = 99

[dakshgiriraj]

did it orally..not bragging abt self...but this was an easy one

[csmoke]

Different method same result .... getting better.

[AdamjacobiGIA]

What an elegant solution! Like many other commenters I took a longer route:

Where b is the uppermost angle of the rightmost isosceles triangle and the two other angles are necessarily 2a, b = 180 - 4a
Since b + a + x must also equal 180, b = 180 - a - x.
Subtracting the two b equations, 3a = x.
On the left triangle, 33 degrees + a + (180-2a) = 180.
Simplifies to 213 - a = 180, or a=33.
x = 3a, so x = 99.

I should keep the Exterior Angle Theorem more readily in mind next time! Thank you for the video!

[vdocrazee]

99 because alpha = 180-147 = 33 and 33+180-66-66+x = 180

[MrPaulc]

Great video. I calculated by a more circuitous route but got the same answer :)

[seroujghazarian]

33+alpha=2alpha
alpha=33°

<=>.x=3alpha=99°

[himo]

33°+α=2α α=33° 2•33°=66°
180°-2•66°=48°
180°-(33°+48°)=99° x=99°