Question

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?

Answer 1

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.

$m\angle QRS=m\angle RPQ+m\angle PQR$       [Exterior angle theorem]

$11x-7=(3x+17)+(3x+11)$

$11x-7=6x+28$

Isolate variable terms.

$11x-6x=7+28$

$5x=35$

Divide both sides by 5.

$x=7$

Therefore, the value of x is 7.

Answer 2

Answer:

7

Delta Math

Step-by-step explanation:

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.