Finding Angles Applying Line of Symmetry

In math, some questions may look difficult at first, but upon further analysis, it may not be so. Understanding the principle of the relevant topics will normally be sufficient to solve these math questions.

Let's look at one example on geometry.

Question: (Diagram 1)
A piece of rectangular paper is folded at one corner with an angle of 74⁰. Determine the angle Y due to this folding.


Diagram 1

Hint: You need to know the principle of "Line of Symmetry".
Solution is right below. But do not waste the chance to challenge yourself before looking at the solution!

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Solution:

We can solve this question by identifying the line of symmetry at the folded line. This symmetrical property will reveal more information and angles later.

But first look at diagram 2 for explanation to answer.


Diagram 2

From diagram 2, you can find the angle Q knowing the fact that the total angle of a triangle is 180⁰.

Therefore,
angle Q = 180⁰- 74⁰ - 90⁰ = 16⁰

In diagram 2, you can see that the line of symmetry (AB) is indicated in red. This line revealed that angle P = ange Q.

Thus, angle P = 16⁰.

Knowing angle Q and angle P, you can now determine angle Y. How?

Angle Y + Angle Q + Angle P = 180⁰.
Angle Y = 180⁰ - angle P - angle Q
Angle Y = 180⁰ - 16⁰ - 16⁰
Angle Y = 148⁰ (Answer)

This solution is not that difficult after all, right? :)

You just need to know the principle of the line of symmetry to extract more information of any hidden angles, and some basic rules of triangle and their angle summation.

For "Line of Symmetry" concept in graphs and its impact, refer to this link.

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