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In the following figure, find πβ π·ππΈ.

In the following figure, find the measure of angle π·ππΈ.

We begin by recalling that the sum of the measures of the angles at a point is 360 degrees. And it is also important to note that we cannot assume that the line from point πΆ to point πΈ is a straight line. So we can therefore not use the properties of supplementary angles. This means that the five angles in our diagram sum to 360 degrees. We can write this as an equation as shown. The measure of angle π·ππΈ plus the measure of angle π΄ππΈ plus 119 degrees plus 76 degrees plus 41 degrees is equal to 360 degrees. Summing the three known angles gives us 236 degrees, and we can therefore simplify our equation. We can then subtract 236 degrees from both sides such that the measure of angle π·ππΈ plus the measure of angle π΄ππΈ is equal to 124 degrees.

At this stage, it may not be clear what to do next. However, letβs consider how the two unknown angles are labeled on the diagram. This notation tells us that the two angles are equal. The line ππΈ is an angle bisector such that the measure of angle π·ππΈ is equal to the measure of angle π΄ππΈ. Since the two angles are equal, we can rewrite our equation as two multiplied by the measure of angle π·ππΈ is equal to 124 degrees. And dividing through by two, the measure of angle π·ππΈ is equal to 62 degrees. As this also means that angle π΄ππΈ measures 62 degrees, we could add these to our diagram and then check that all five angles sum to 360 degrees.

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