Question

Find m∠S in rhombus RSTU

Answer 1

In a rhombus, opposite angles are equal, therefore:

m∠S = m∠U = a + 62 degrees

And

m∠R = 2a - 80 degrees

The opposite angles of a rhombus are supplementary, meaning they add up to 180 degrees. So,

m∠S + m∠R = 180 degrees

Therefore,

a + 62 + 2a - 80 = 180

Solving for a, we get:

a = 59

So,

m∠S = a + 62 = 59 + 62 = 121 degrees