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Altitudes AD and BE of triangle ABC intersect at H. If angle BAC = 54 and angle ABC = 52, then what is angle AHB?

 

- Daisy

dierdurst  Aug 20, 2018
edited by dierdurst  Aug 22, 2018
edited by dierdurst  Aug 24, 2018

Best Answer 

 #1
avatar+7336 
+4

Here's a rough drawing of the triangle:

 

 

Since the sum of the angle measures in a triangle is  180°...

m∠BCA  =  180° - 54° - 52°   =   74°

 

Now look at quadrilateral CDHE.

Since the sum of the angle measures in a quadrilateral is  360°...

m∠DHE  =  360° - 74° - 90° - 90°  =  106°

 

And since  ∠DHE  and  ∠AHB  are vertical angles, they have the same measure.

m∠AHB  =  m∠DHE  =  106°

hectictar  Aug 20, 2018
 #1
avatar+7336 
+4
Best Answer

Here's a rough drawing of the triangle:

 

 

Since the sum of the angle measures in a triangle is  180°...

m∠BCA  =  180° - 54° - 52°   =   74°

 

Now look at quadrilateral CDHE.

Since the sum of the angle measures in a quadrilateral is  360°...

m∠DHE  =  360° - 74° - 90° - 90°  =  106°

 

And since  ∠DHE  and  ∠AHB  are vertical angles, they have the same measure.

m∠AHB  =  m∠DHE  =  106°

hectictar  Aug 20, 2018

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