Answer:
m∠2 = 130°
m∠3 = 25°
m∠4 = 25°
Explanation:
Opposite angles of rhombi are congruent. Therefore,
m∠1 = m∠2 = 130°
The measures of the interior angles of a triangle add to 180°. Using this information, along with the isosceles triangle theorem, we can solve for m∠3 (which is also congruent to m∠4):
m∠2 + 2(m∠3) = 180°
↓ substituting in m∠2
130° + 2(m∠3) = 180°
↓ subtracting 130° from both sides
2(m∠3) = 50°
↓ dividing both sides by 2
m∠3 = 25°
m∠3 = m∠4 = 25°