An isosceles triangle has an angle that measures 42 degrees. What other angles could be in that isosceles triangle?

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Answer 1 · 2017-03-23T13:35:22

See explanation.

If a triangle is isosceles then it has 2 identical angles and the third different one. So in the given example we have to check 2 cases:

I. The given angle is opposite to the base

Then we have the angles: #42,x,x#, where #x# is the angle at the base.

To calcu;late #x# we use the property saing that the sum of angles in any triangle is equal to 180.

#2x+42=180#

#2x=138#

#x=69#

So the angles are: #42^o,69^o# and #69^o#

II. The given angle is one of the angles at the base

Then the angles are #42,42,x#. We have to calculate the angle opposite to the base. As before we use the sum of angles identity:

#2*42+x=180#

#84+x=180#

#x=96#

The angles are: #42^o,42^o# and #96^o#