Question

1. calculate the value of x.

le feh after a reflection across line hf. select all the
parts of congruent triangles being congruent.

Explanation:

Step1: Use the triangle angle - sum property

In \(\triangle PQR\), since \(PR = PQ\) (marked with equal signs), \(\triangle PQR\) is an isosceles triangle. The sum of the interior angles of a triangle is \(180^{\circ}\). Let \(\angle R=\angle Q\).
We know that \(\angle P = 40^{\circ}\), and \(\angle R+\angle Q+\angle P=180^{\circ}\). Substituting \(\angle Q = 2x^{\circ}\) and \(\angle R = 2x^{\circ}\) (because \(PR = PQ\)) into the angle - sum formula: \(2x+2x + 40=180\).

Step2: Simplify the equation

Combine like terms: \(4x+40 = 180\).
Subtract 40 from both sides of the equation: \(4x=180 - 40\), so \(4x=140\).

Step3: Solve for \(x\)

Divide both sides of the equation \(4x = 140\) by 4: \(x=\frac{140}{4}=35\).

Answer:

\(x = 35\)