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BaLLatris [955]
3 years ago
15

Solve for x,y, and z.

Mathematics
1 answer:
Ann [662]3 years ago
6 0

The given triangle is isosceles, so the two remaining angles in the triangle both have measure <em>xº</em>. The interior angles of any triangle sum to 180º, so that

58º + <em>xº</em> + <em>xº</em> = 180º

58 + 2<em>x</em> = 180

2<em>x</em> = 122

<em>x</em> = 61

Angles <em>y</em> and <em>z</em> are supplementary to angle <em>x</em>, so that

<em>xº</em> + <em>yº</em> = 180º

and

<em>xº</em> + <em>zº</em> = 180º

and consequently, <em>y</em> = <em>z</em>. In particular, we get

<em>y</em> = 180 - 61

<em>y</em> = 119

and so

<em>z</em> = 119

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