Question

If RSTU is a rhombus, find the measure of angle RUT.

Answer 1

Finding x:

We know that the diagonals of a rhombus bisect its angles

So, since US is a diagonal of the given rhombus:

∠RUS = ∠TUS

10x - 23 = 3x + 19                      [replacing the given values of the angles]

7x - 23 = 19                                [subtracting 3x from both sides]

7x = 42                                       [adding 23 on both sides]

x = 6                                           [dividing both sides by 7]

Finding ∠RUT:

We can see that:

∠RUT = ∠RUS + ∠TUS

Since we are given the values of ∠RUS and ∠TUS:

∠RUT = (10x - 23) + (3x + 19)

∠RUT = 13x - 4

We know that x = 6:

∠RUT = 13(6)-  4

∠RUT = 74°