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In triangle XYZ, the bisector of angle YXZ meets YZ at W.  If angle X = 60, angle Y = 45, and XW = 24, then find angle XWZ.

 

\(\phantom{find WY}\)

 

\(\phantom{find ZW}\)

 

\(\phantom{find the area of triangle XYZ}\)

 Jun 22, 2022

Best Answer 

 #1
avatar+589 
+1

We know that the three angles of a triangle sum up to 180, so angle Z = 75. We know that X = 60, so the angle bisector must split YXZ into 30 and 30. Now we can see that the angle bisector has split triangle XYZ into two smaller triangles, one being XWZ. Again, we can use our knowledge of the sum of triangle angles, so X + W + Z = 180 = 30 + 75 + W

 

So angle XWZ = \(\boxed{95}\)

 Jun 22, 2022
 #1
avatar+589 
+1
Best Answer

We know that the three angles of a triangle sum up to 180, so angle Z = 75. We know that X = 60, so the angle bisector must split YXZ into 30 and 30. Now we can see that the angle bisector has split triangle XYZ into two smaller triangles, one being XWZ. Again, we can use our knowledge of the sum of triangle angles, so X + W + Z = 180 = 30 + 75 + W

 

So angle XWZ = \(\boxed{95}\)

SparklingWater2 Jun 22, 2022

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