Question

Use a definition, postulate, or theorem to find the value of x in the figure described.

∠ABC and ∠CBD are a linear pair. If m∠ABC = m∠CBD = (3x − 3)°, find x.

Select each definition, postulate, or theorem you will use.

A Linear Pair Theorem
B definition of a linear pair
C definition of an angle bisector
D Angle Addition Postulate

Answer 1

We know that ∠ABC and ∠CBD are a linear pair. A linear pair includes angles that are formed when two lines intersect.

Linear Pair Theorm states that any 2 angles forming a linear pair are supplementary, i.e. their sum is equal to 180 degree

We also know that m∠ABC = m∠CBD = (3x-3)°

⇒ m∠ABC + m∠CBD = 180°

⇒ (3x-3)° + (3x-3)° = 180°

⇒ (6x-6)° = 180°

⇒ x = 31°

So in the above we have used A and B definition / theorem to determine the answer