Answer:
∠QRT = 62°
∠QRS = 152°
∠RSQ = 14°
Step-by-step explanation:
In parallelograms, opposite sides have the same measure. So, if PQRT is a parallelogram, then ∠QPT is equal to ∠QRT. Then:
∠QRT = ∠QPT
∠QRT = 62°
On the other hand, ∠QRS is equal to the sum of angles QRT and TRS, so:
∠QRS = ∠QRT + ∠TRS
∠QRS = 62° + 90°
∠QRS = 152°
Finally, QRS is an isosceles triangle because it has two equal sides, QR = RS. In isosceles triangles, there are two equal angles, so ∠RSQ = ∠RQS.
Additionally, the sum of the interior angles of a triangle is equal to 180, so we can write the following equation:
∠RSQ + ∠RQS + ∠QRS = 180°
Since ∠RSQ = ∠RQS, we can rewrite the equation as follows:
∠RSQ + ∠RSQ + ∠QRS = 180°
2∠RSQ + ∠QRS = 180°
Finally, replacing ∠QRS by 152 and solving for ∠RSQ, we get:
2∠RSQ + 152 = 180
2∠RSQ + 152 - 152 = 180 - 152
2∠RSQ = 28
2∠RSQ/2 = 28/2
∠RSQ = 14°
Therefore, the answers are:
∠QRT = 62°
∠QRS = 152°
∠RSQ = 14°