Question

find x and y in the following figures WITH REASONS NO DIRECT ANSWER ​

Answer 1

Answer:

x = 45°

y = °

Step-by-step explanation:

Given:

PQ is bisected by point A

QR is bisected by point C

PQ = QR (all sides are equal in a square)

Then, PA = QC (common)

Thus, ∆AQC is an isosceles triangle

angle AQC = 90° (the interior angles of a square measure 90°)

Then, the other two angles are (QAC & QCA) are 45° each (angle sum prop. of a triangle & any two interior angles of an isosceles triangle are equal)

In the rectangle PQCB, angle QCB measures 90° (interior angles of a rectangle measure 90°)

Then, y° + 60° = 90°

=> y° = 90°- 60°

=> y° = 30° (ans 1)

In the rectangle PQCB:

QC = DB (opp. sides of a rectangle are equal)

angles ADB & CQA are 90° each (interior angles of a rectangle measure 90°)

DA = QA (given)

Then ∆ADB is congruent to ∆AQC (under SAS criteria)

Then, angle DBE = angle QCE (corresponding parts of congruent triangles)

x° = 45° (ans 2)p