Find the value of z in parallelogram RSTU.

T
U
R
S
z+60°
z
z=
°

1 answer

In a parallelogram, opposite angles are equal, and consecutive angles are supplementary (their sum is \(180^\circ\)).

Given the angles:

  • Let's assume \(\angle R = z + 60^\circ\)
  • \(\angle S = z\)

Since R and S are consecutive angles, we can write the equation:

\[ (z + 60^\circ) + z = 180^\circ \]

Now, combine like terms:

\[ 2z + 60^\circ = 180^\circ \]

Next, subtract \(60^\circ\) from both sides:

\[ 2z = 120^\circ \]

Now, divide by 2:

\[ z = 60^\circ \]

So the value of \(z\) in the parallelogram RSTU is \(60^\circ\).