Video: Finding the Size of an Angle in a Triangle That Has a Relation with Another Angle

In the figure, △𝐷𝐡𝐢 is symmetrical about line 𝐿. If π‘šβˆ πΆ = 69Β°, what is π‘šβˆ π΄π΅π·?

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Video Transcript

In the figure, triangle 𝐷𝐡𝐢 is symmetrical about line 𝐿. If the measure of angle 𝐢 is 69 degrees, what is the measure of angle 𝐴𝐡𝐷?

We’re told that triangle 𝐷𝐡𝐢 is symmetrical about line 𝐿. So it’s a mirror image over this line. We are also told that the measure of angle 𝐢 is 69 degrees, and we want to find the measure of angle 𝐴𝐡𝐷.

It’s very important that triangle 𝐷𝐡𝐢 is symmetrical about line 𝐿, because if the measure of angle 𝐢 is 69 degrees, the measure of angle 𝐢𝐷𝐡 must also be 69 degrees. And this is because if we would take our yellow triangle and fold it over the blue line, those angles would land on top of each other, should they- should be the exact same 69 degrees. And this is helpful for a few reasons.

All angles of triangle 𝐷𝐡𝐢 must add up to be 180 degrees, because a triangle always does. So we can find this last angle of the triangle by setting 69 plus 69 plus π‘₯ equal to 180 degrees. 69 plus 69 is 138, and if we subtract 138 from both sides of the equation, we find that π‘₯ is equal to 42 degrees.

So how will this help us find the measure of angle 𝐴𝐡𝐷? Well, the measure of angle 𝐡 completely is 90 degrees, because of that box. So if we can call our missing angle 𝑦, then that angle plus 42 should equal 90. So to solve for 𝑦, we need to subtract 42 from both sides of the equation, resulting in that angle equaling 48 degrees. Therefore, the measure of angle 𝐴𝐡𝐷 is equal to 48 degrees.

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