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, adjacent angles are supplementary ($\angle R+\angle T = 180^{\circ}$), and opposite angles are equal ($\angle R=\angle Q$, $\angle S=\angle T$).

Step2: Calculate $\angle S$

Since $\angle T = 135^{\circ}$, and $\angle S+\angle T=180^{\circ}$, then $\angle S=180^{\circ}- 135^{\circ}=45^{\circ}$.

Step3: Determine $\angle R$ and $\angle Q$

Because $\angle R=\angle Q$ and $\angle R = 45^{\circ}$ (opposite angles of parallelogram $RQTS$ with $\angle S = 45^{\circ}$)

Answer:

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