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° = 158, the value of d° is 158.

A circle is a figure in which each point around its perimeter is an equal distance from the center. The radius of a circle is the distance between the center and any point along its perimeter. A chord is a line segment that connects any two points along its perimeter. The diameter of a circle is the length of a chord that passes through the center of the circle and equals twice the circle's radius (2r).

A circle is a figure in which each point around its perimeter is an equal distance from the center. The radius of a circle is the distance between the center and any point along its perimeter. A chord is a line segment that connects any two points along its perimeter. The diameter of a circle is the length of a chord that passes through the center of the circle and equals twice the circle's radius (2r).

The first step to solve a quadratic expression that's not set to zero is to solve the equation so that it is set to zero:

b² - 16b + 31 = -4b + 4
b² - 16b + 31 - 4 = -4b
b² - 16b + 4b + 27 = 0
b² - 12b + 27 = 0

Next, factor the quadratic equation:

b² - 12b + 27 = 0
(b - 3)(b - 9) = 0

For this expression to be true, the left side of the expression must equal zero. Therefore, either (b - 3) or (b - 9) must equal zero:

If (b - 3) = 0, b must equal 3
If (b - 9) = 0, b must equal 9

So the solution is that b = 3 or 9

An isosceles triangle has two sides of equal length. An equilateral triangle has three sides of equal length. In a right triangle, two sides meet at a right angle.