Triangle Angle Calculation: Find X and Y Given 43° and 47° Angles

Triangle Angle Sum with Right Triangles

Calculate the values of x and y.

AAABBBDDDCCC43°47°yx

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Step-by-step video solution

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00:00 Find X,Y
00:10 The sum of angles in a triangle equals 180
00:21 Collect terms and isolate X
00:41 This is the value of Y
00:46 We'll use exactly the same method to find X
01:01 Collect terms and isolate X
01:20 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Calculate the values of x and y.

AAABBBDDDCCC43°47°yx

2

Step-by-step solution

First, let's note that in triangle ACB we are given two angles.

Angle ABC equals 47 degrees, angle ACB equals 90 degrees.

Since the sum of angles in a triangle equals 180, we can calculate angle BAC and find the value of Y as follows:

1809047=43 180-90-47=43

Now let's look at triangle ACD, where we are also given two angles.

Angle CAD equals 43 degrees, angle ACD equals 90 degrees.

Since the sum of angles in a triangle equals 180, we can calculate angle ADC and find the value of X as follows:

1809043=47 180-90-43=47

3

Final Answer

y=43, x=47

Key Points to Remember

Essential concepts to master this topic
  • Angle Sum Rule: All triangle angles always total exactly 180 degrees
  • Right Triangle Method: Calculate unknown angle as 18090given angle 180 - 90 - \text{given angle}
  • Check: Verify both triangles: 43° + 90° + 47° = 180° ✓

Common Mistakes

Avoid these frequent errors
  • Confusing vertical angles with triangle angles
    Don't assume y equals the 47° angle just because they look similar = wrong values! These are different triangles with different angle relationships. Always use the 180° rule within each specific triangle.

Practice Quiz

Test your knowledge with interactive questions

Indicates which angle is greater

FAQ

Everything you need to know about this question

Why does y equal 43° and not 47°?

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Look carefully at triangle ABC! You have a 90° right angle at C and 47° at B. Using the triangle angle sum: y=1809047=43° y = 180 - 90 - 47 = 43° .

How do I know which triangle to work with first?

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Start with whichever triangle has two known angles. In this case, triangle ABC has 90° and 47°, so find y first. Then use that result in triangle ACD.

What's the role of the right angle marker?

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The small square at point C shows a 90° right angle. This is crucial information - without it, you couldn't solve for the unknown angles!

Why is x = 47° the same as the other given angle?

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It's not a coincidence! In triangle ACD, you have 90° at C and 43° at A (which equals y). So x=1809043=47° x = 180 - 90 - 43 = 47° .

Can I solve this problem in a different order?

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Not really - you need to find y first because it becomes a known angle in triangle ACD. Always solve triangles in the order that gives you the information you need!

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