Can you Find Angle X? Step-by-step Explanation — Transcript

Step-by-step solution to find angle X in a compound triangle shape using isosceles properties and exterior angle theorem.

Key Takeaways

Use properties of isosceles triangles to identify equal angles.
Apply the exterior angle theorem to relate unknown angles to known angles.
Set up equations based on triangle angle relationships to solve for unknowns.
Angle X in the given compound shape is found to be 33 degrees.
Careful labeling and stepwise reasoning simplify complex geometric problems.

Summary

The video explains how to find angle X in a compound shape made of multiple triangles.
Side lengths AB, BC, and BD are equal, and angle ABP is given as 66 degrees.
The figure is not necessarily to scale, and angles B and C are not assumed to be 90 degrees.
Angle BCP is defined as alpha, and angle BCD is expressed as X plus alpha.
Triangles BCD and ABC are identified as isosceles, leading to equal base angles.
The exterior angle theorem is applied to relate angle X to interior angles alpha and beta.
Equations are formed using exterior angles in triangles ABP and DPC.
By equating expressions for angle BPC, the equation 2X + alpha = alpha + 66 degrees is derived.
Solving the equation yields angle X as 33 degrees.
The video concludes with the final answer and encourages viewers to subscribe.

Full Transcript — Download SRT & Markdown

Speaker A

Welcome to PreMath. In this video tutorial, we have got this compound shape that consists of multiple triangles as you can see in this figure, such that these side lengths AB, this side length BC and this side length BD are equal in length and moreover, this angle ABP is 66 degrees and now we are going to calculate this angle X.

Speaker A

So let's go ahead and get started with the solution. So before we proceed, let me make it very clear that this figure may not be 100% true to the scale and one more thing, we do not assume that these two angles B and C are 90 degrees.

Speaker A

And here's our very first step. Let's assume that this angle BCP, I am going to call this angle alpha, then this angle BCD is going to be X plus alpha.

Speaker A

And now let's focus on this triangle BCD and this is an isosceles triangle since this side length BC is equal to this side length BD. So therefore, if this angle is X plus alpha, then this angle has got to be X plus alpha as well.

Speaker A

And now let's focus on this triangle ABC and we can see that this is an isosceles triangle as well, since this side length AB is equal to this side length BC.

Speaker A

So therefore, if this angle is alpha, then this angle has got to be alpha as well. And here's our next step. Let's recall exterior angle property.

Speaker A

And here's our exterior angle theorem. The exterior angle of a triangle is equal to the sum of two opposite interior angles.

Speaker A

In our case, this X is our exterior angle and that is equal to the sum of two opposite interior angles alpha and beta.

Speaker A

And now let's focus on this triangle ABP, our exterior angle, this exterior angle is going to be the sum of these two opposite interior angles.

Speaker A

So therefore, this angle is going to become alpha plus 66 degrees. And let me go ahead and call this as an equation number one. And now let's focus on this triangle DPC and we can see that our exterior angle for this triangle is going to be this angle as well, which is BPC.

Speaker A

And this angle is going to be equal to the sum of these two opposite interior angle X and this angle X plus alpha, so X plus X is going to give us 2X plus alpha. And no wonder I wrote down this one as angle BPC equals to 2X plus alpha.

Speaker A

And let me go ahead and call this equation as number two. And now let's go ahead and compare these equations one and two, since the left hand side is same, so we can equate these right hand side as well. So therefore, I can write 2X plus alpha equals to alpha plus 66 degrees.

Speaker A

So we ended up with 2X equal to 66 degrees. Let's divide both side by two, that means our X value turns out to be simply 33 degrees.

Speaker A

So that's our angle X turns out to be 33 degrees. Thanks for watching and please don't forget to subscribe to my channel for more exciting videos.

Topics:angle Xisosceles triangleexterior angle theoremgeometry problemtriangle anglesPreMath tutorialangle calculationcompound shapestep-by-step solutionmath tutorial

How is angle X related to the other angles in the figure?

Angle X is an exterior angle related to the sum of two opposite interior angles alpha and beta in the triangles considered.

Why are triangles BCD and ABC considered isosceles?

Because the side lengths BC and BD are equal, and AB and BC are equal respectively, making triangles BCD and ABC isosceles with equal base angles.

What is the final value of angle X?

The final calculated value of angle X is 33 degrees after applying the exterior angle theorem and solving the resulting equation.

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