# Question Video: Using the Properties of Similar Triangles to Find an Unknown Angle Measure Mathematics

Given that π΄π΅πΆ is similar to πππ, find the value of π₯.

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### Video Transcript

Given that π΄π΅πΆ is similar to πππ, find the value of π₯.

π΄π΅πΆ and πππ are both triangles. Since these are similar triangles, the properties of similar polygons will apply. In similar polygons, corresponding angles are congruent, and corresponding sides are proportional. Here, weβll be primarily concerned with the angles. And our first job will be identifying which of the angles in these triangles are corresponding.

Based on the naming convention, since triangle π΄π΅πΆ is similar to triangle πππ, the angle at vertex π΄ will be corresponding to the angle at vertex π. Since these two angles are corresponding, we can say that angle π must be 54 degrees. We donβt need it to solve this question, but we can go ahead and identify that the angle at vertex π΅ corresponds to the angle at vertex π and the angle at vertex πΆ corresponds to the angle at vertex π. This makes the angle π΄πΆπ΅ 85 degrees.

To solve for π₯, we remember that the three angles inside a triangle sum to 180 degrees. And therefore, 54 plus two π₯ plus two plus 85 equals 180. Combining like terms, we reduce this to two π₯ plus 141 equals 180. Subtracting 141 from both sides gives us two π₯ equals 39. And dividing through by two, we find that π₯ must be equal to 19.5.

If we plug in 19.5 into two π₯ plus two, we find that the angle at vertex π is 41 degrees, which would also be the case for the angle at vertex π΅. Itβs possible to check your working by adding 41, 54, and 85 to confirm that they equal 180 degrees, which they do. Therefore, we can say that π₯ equals 19.5.