This is what a full credit paper looks like. Read the problem, then compare
every box with your own.
The Problem
In the stained glass window below, angle EBD and angle DBA are complementary.
C, B and A lie on a straight line. The measure of angle DBA is
30°.
Find the measure of angle EBD and the measure of angle CBD.
Orange = the angle you are given. Blue = first answer. Green = second answer. Purple = the 90° that complementary gives you.
Box 1 — I know
half a point
The measure of angle DBA is 30°. This is given.
Angle EBD and angle DBA are complementary. Complementary angles add to 90°.
C, B and A are on a straight line. A straight line is 180°.
Angle DBA and angle CBD together make that straight line.
Box 2 — I need to find out
half a point
I need to find the measure of angle EBD and the measure of angle CBD,
in degrees.
Box 3 — Steps
2 points · the biggest box
Part 1 — find angle EBD
Complementary means the two angles add to 90°.
angle EBD + angle DBA = 90°
angle EBD + 30 = 90
90 − 30 = 60 angle EBD = 60°
Part 2 — find angle CBD
C, B, A is a straight line, so it measures 180°.
angle CBD + angle DBA = 180°
angle CBD + 30 = 180
180 − 30 = 150 angle CBD = 150°
Part 3 — check both answers60 + 30 = 90
(correct, they are complementary) 150 + 30 = 180
(correct, it is a straight line)
Box 4 — Answer
2 points
angle EBD = 60° ✓
angle CBD = 150° ✓
Why this earns all 5 points
Box 1 has three facts, not one. Most papers wrote only "angle DBA = 30°".
The two definitions — complementary = 90° and straight line = 180° — are what
actually solve the problem, so they belong here.
Box 2 names both angles. Not "find the angles" and not a list of points.
Angle EBD and angle CBD, by name.
Box 3 shows the subtraction. Writing 60 and 150 without 90 − 30 and
180 − 30 on the page earns almost nothing. Steps is the 2-point box.
Box 3 also checks the work. 60 + 30 = 90 and 150 + 30 = 180 prove both answers.
This is the step that separates a 2 from a 1 and a half.
Box 4 gives labeled answers with units. Which number goes with which angle,
and the degree symbol on both.
Two mistakes to avoid
1. Do not add 90 + 60 to get 150. It gives the right number here only by luck,
because 60 happens to be the other answer. Change the given angle to 40° and it falls apart.
The real rule is 180 − the given angle.
2. Do not measure with a protractor. The diagram is not drawn to scale. These angles
are found by subtracting, not by measuring.
How to remember it: complementary is a corner, so subtract from 90. A straight line is a street, so subtract from 180.