Question 1042108
In △XY Z, it is given that XY = YZ and that ∠Y = 42°
. Find the measure of ∠X.

{{{drawing(300,300,-.3,1,-.2,1,locate(.31,.8,"42°"),
locate(0,0,X),locate(.71,0,Z),locate(.345,.99,Y),
triangle(0,0,cos(69*pi/180),sin(69*pi/180),.7167358991,0) )}}}
<pre>
Since XY = YZ, we know that &#916;XYZ is isosceles and we have
proved that the base angles of an isosceles triangle are
equal.  So &#8736;X = &#8736;Z

We have also proved that the sum of the three interior angles of 
any triangle is 180°.

Therefore &#8736;X + &#8736;Y + &#8736;Z = 180°, and since &#8736;X = &#8736;Z,
we can substitute &#8736;X for &#8736;Z, and also 42° for &#8736;Y and get:

          &#8736;X + 42° + &#8736;X = 180°

              2&#8736;X + 42° = 180°

Subtract 42° from both sides gives:

                    2&#8736;X = 138°

Dividing both sides by 2

                     &#8736;X = 69°

Edwin</pre></b>