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: $42, x, x$ $42,x,x$ , where $x$ $x$ is the angle at the base.

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

$2 x + 42 = 180$ $2x+42=180$

$2 x = 138$ $2x=138$

$x = 69$ $x=69$

So the angles are: $42^{o}, 69^{o}$ $42^o,69^o$ and $69^{o}$ $69^o$

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

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

$2 \cdot 42 + x = 180$ $2*42+x=180$

$84 + x = 180$ $84+x=180$

$x = 96$ $x=96$

The angles are: $42^{o}, 42^{o}$ $42^o,42^o$ and $96^{o}$ $96^o$