Answer:
x = 10
y = 15
Explanation:
Start with y.
The smaller triangle has a right angle and two congruent legs.
Since the legs are congruent, then the opposite angles are also congruent.
The measures of the 3 angles of the right triangle are:
3y, 3y, 90
The sum of the measures of the angles of a triangle is 180°.
3y + 3y + 90 = 180
6y + 90 = 180
6y = 90
y = 15
The larger triangle has 2 congruent sides. The opposite angles are congruent. Each of the congruent angles measures 2x + 3y. The angle above measures 50°.
2x + 3y + 2x + 3y + 50 = 180
4x + 6y + 50 = 180
4x + 6y = 130
We know from above that y = 15.
4x + 6(15) = 130
4x + 90 = 130
4x = 40
x = 10