Question

how many degrees is angle \x\ if \\(b = 110^{\circ}\\)?

a \\(45^{\circ}\\)
b \\(70^{\circ}\\)
c \\(90^{\circ}\\)
d \\(270^{\circ}\\)

Explanation:

⚡ Using what you learned: properties of quadrilaterals

Step 1: Identify the quadrilateral type

The given figure has opposite sides that are equal in length, as indicated by the matching tick marks (single tick marks on the left and right sides, and double tick marks on the top and bottom sides). A quadrilateral with opposite sides equal is a parallelogram.

Step 2: Apply consecutive angles property

In a parallelogram, consecutive angles (angles next to each other) are supplementary, meaning they add up to \( 180^\circ \).

$$ x + B = 180^\circ $$

Step 3: Calculate the value of \( x \)

Substitute the given value \( B = 110^\circ \) into the equation:

$$ x + 110^\circ = 180^\circ $$

$$ x = 180^\circ - 110^\circ $$

$$ x = 70^\circ $$

Answer:

B) \( 70^\circ \)