For parallel lines with a transversal, the following relationships apply:

• angles in the same position on different parallel lines equal each other (a° = w°, b° = x°, c° = z°, d° = y°)
• alternate interior angles are equal (a° = z°, b° = y°, c° = w°, d° = x°)
• all acute angles (a° = c° = w° = z°) and all obtuse angles (b° = d° = x° = y°) equal each other
• same-side interior angles are supplementary and add up to 180° (e.g. a° + d° = 180°, d° + c° = 180°)

Applying these relationships starting with y° = 151, the value of c° is 29.

To solve this equation, isolate the variable for which you are solving (a) on one side of the equation and put everything else on the other side.

-4a - 7y = -5a - 6y - 5
-4a = -5a - 6y - 5 + 7y
-4a + 5a = -6y - 5 + 7y
a = y - 5

An exterior angle of a triangle is equal to the sum of the two interior angles that are opposite:

d° = b° + c°

To find angle c, remember that the sum of the interior angles of a triangle is 180°:

180° = a° + b° + c°
c° = 180° - a° - b°
c° = 180° - 69° - 31° = 80°

So, d° = 31° + 80° = 111°

A shortcut to get this answer is to remember that angles around a line add up to 180°:

a° + d° = 180°
d° = 180° - a°
d° = 180° - 69° = 111°

A parallelogram is a quadrilateral with two sets of parallel sides. Opposite sides (a = c, b = d) and angles (red = red, blue = blue) are equal. The area of a parallelogram is base x height and the perimeter is the sum of the lengths of all sides (a + b + c + d).

The area of a triangle is equal to ½ base x height:

a = ½bh
a = ½ x 9 x 9 = \( \frac{81}{2} \) = 40\(\frac{1}{2}\)