Question

for the following parallelogram, label all angles: drag & drop the answer 135° 45° 180° 55° 35° note: use ctrl+d to drag the option via keyboard (parallelogram with vertices r, q, t, s; angle at t is 135°, other angles to label)

Explanation:

Step1: Properties of parallelogram

In a parallelogram, consecutive angles are supplementary ($\angle S+\angle T = 180^{\circ}$). Given $\angle T=135^{\circ}$, then $\angle S=180^{\circ}- 135^{\circ}=45^{\circ}$.

Step2: Opposite angles property

In a parallelogram, opposite angles are equal. So $\angle R=\angle T = 135^{\circ}$ and $\angle Q=\angle S = 45^{\circ}$.

Answer:

$\angle S = 45^{\circ}$, $\angle R = 135^{\circ}$, $\angle Q = 45^{\circ}$