Example Data Table
| Case |
Given Data |
Method |
Angle A |
Angle B |
Result |
| 1 |
Angle A = 70° |
Missing angle |
70° |
110° |
Valid linear pair |
| 2 |
125° and 55° |
Check pair |
125° |
55° |
Valid linear pair |
| 3 |
Ratio 2:3 |
Ratio split |
72° |
108° |
Valid linear pair |
| 4 |
3x + 15 and 2x + 40 |
Algebra |
90° |
90° |
x = 25 |
Formula Used
A linear pair contains two adjacent angles. Their non-common arms form a straight line. Because a straight line measures 180 degrees, the two angles are supplementary.
Main formula:
Angle A + Angle B = 180°
Missing angle:
Missing Angle = 180° − Known Angle
Ratio formula:
Angle A = 180 × Ratio A ÷ Total Ratio Parts
Angle B = 180 × Ratio B ÷ Total Ratio Parts
Algebraic formula:
If Angle A = ax + b and Angle B = cx + d, then:
(ax + b) + (cx + d) = 180
x = (180 − b − d) ÷ (a + c)
How to Use This Calculator
Select the calculation type first. Choose missing angle when one angle is known. Choose check two angles when both angles are given. Choose ratio when the angles are written as parts. Choose algebra when both angles contain x.
Enter all needed values. Select degrees or radians. Set decimal places for rounded answers. Use tolerance when checking two angles with decimals. Press calculate. The result appears above the form. Use the CSV or PDF buttons to save the answer.
Understanding Linear Pair of Angles
What Is a Linear Pair?
A linear pair is a pair of adjacent angles. They share one common side. Their other sides point in opposite directions. These opposite sides create a straight line. A straight line always measures 180 degrees. So, the two angles in a linear pair always add to 180 degrees.
Why This Calculator Helps
This calculator is useful for geometry work. It can find a missing angle. It can also check whether two angles form a linear pair. It supports ratios and algebraic expressions. This makes it helpful for school problems, worksheets, and quick verification.
Finding a Missing Angle
When one angle is known, the second angle is easy to find. Subtract the known angle from 180 degrees. For example, if one angle is 65 degrees, the other angle is 115 degrees. Their sum is 180 degrees, so they can form a linear pair.
Checking Two Angles
Sometimes both angles are already given. In that case, add them together. If the sum is 180 degrees, the pair is valid. If the sum is not 180 degrees, the angles are not a linear pair. A small tolerance can help when decimal values are used.
Using Ratios
Some questions give angles as a ratio. A ratio of 2:3 means the straight angle is split into five equal parts. Each part is worth 36 degrees. So the angles are 72 degrees and 108 degrees. This method is common in word problems.
Using Algebra
Algebraic angle problems include expressions like 3x + 15 and 2x + 40. Add both expressions and set the total equal to 180. Solve for x. Then place x back into each expression. This gives the final angle measures.
Practical Use
Linear pairs appear in diagrams, proofs, construction sketches, and coordinate geometry. They also support reasoning about supplementary angles. This calculator shows each step, so the answer is easier to understand and check.
FAQs
What is a linear pair of angles?
A linear pair is two adjacent angles whose outer sides form a straight line. Their measures always add up to 180 degrees.
Are linear pair angles always supplementary?
Yes. Linear pair angles are always supplementary because they form a straight angle. Their total measure is 180 degrees.
Can both angles in a linear pair be equal?
Yes. If both angles are equal, each angle is 90 degrees. Together, they form a straight angle of 180 degrees.
How do I find the missing angle?
Subtract the known angle from 180 degrees. The result is the missing angle in the linear pair.
Can this calculator check two given angles?
Yes. Select the check option. Enter both angles. The calculator adds them and compares the sum with 180 degrees.
How does the ratio option work?
The ratio option divides 180 degrees by the total ratio parts. It then multiplies each part by its matching ratio value.
Can I solve expressions with x?
Yes. Enter coefficients and constants for both angle expressions. The calculator solves x and then finds both angles.
Why is tolerance included?
Tolerance helps when checking decimal answers. It allows tiny rounding differences without marking a correct pair as wrong.