Question

given m||n, find the value of x.
a) what type of angle pair is shown?
alternate interior
alternate exterior
same side interior
same side exterior
corresponding
linear pair
vertical
b) are the angles congruent or supplementary
congruent (∠1 = ∠2)
supplementary (∠1 + ∠2 = 180°)
c) solve for x.
check your work: you are correct!
youve tried 1 times.

Explanation:

Step1: Identify angle - pair type

Since the angles are on the same side of the transversal and inside the parallel lines \(m\) and \(n\), they are same - side interior angles.

Step2: Determine angle relationship

Same - side interior angles of parallel lines are supplementary, so \((7x + 10)+(6x+3)=180\).

Step3: Simplify the equation

Combine like terms: \(7x+6x + 10 + 3=180\), which gives \(13x+13 = 180\).

Step4: Isolate the variable term

Subtract 13 from both sides: \(13x=180 - 13\), so \(13x=167\).

Step5: Solve for x

Divide both sides by 13: \(x=\frac{167}{13}\approx12.85\).

Answer:

a) Same Side Interior
b) Supplementary (\(\angle1+\angle2 = 180^{\circ}\))
c) \(x=\frac{167}{13}\)