In ΔPQR, \overline{PR} PR is extended through point R to point S, \text{m}\angle QRS = (11x-7)^{\circ}m∠QRS=(11x−7) ∘ , \text{m}\angle RPQ = (3x+17)^{\circ}m∠RPQ=(3x+17) ∘ , and \text{m}\angle PQR = (3x+11)^{\circ}m∠PQR=(3x+11) ∘ . What is the value of x?X?

Given:

In ΔPQR, PR is extended through point R to point S.

m∠QRS=(11x−7)° , m∠RPQ=(3x+17)° , and m∠PQR=(3x+11)°.

To find:

The value of x.

Solution:

Using the given information, we can draw a diagram as shown below.

From the diagram, it is clear that ∠QRS is an exterior angle and ∠RPQ and ∠PQR are opposite interior angles.

      [Exterior angle theorem]

Isolate variable terms.

Divide both sides by 5.

Therefore, the value of x is 7.

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step-by-step explanation:

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