Answer
The measures of the angles are:
$\\\\100^o,100^o, 110^o, \text{ and } 50^o$
Work Step by Step
Represent the unknown.
$\\\\$Let x=measure of each of the two congruent angles
$\\x+10$=measure of the third angle
$\\0.5x$=measure of the fourth angle.
$\\\\\\$The sum of the four angles is 360 therefore:
$\\\\x+x+(x+10)+0.5x=360
\\\\3.5x+10=360
\\\\3.5x=360-10
\\\\3.5x=350
\\\\x=\frac{350}{3.5}
\\\\x=100$
$\\\\\\$Thus,
$\\\\x+10=100+10=110
\\\\0.5x = 0.5(100)=50$
