Triangle and Straight-Line Angles

What you’ll learn

Find an unknown angle using angle sums.

រកមុំមិនស្គាល់ដោយផលបូកមុំ។

Meaning and use

Angles measure turning. In a flat Euclidean triangle, the three interior angles sum to 180 degrees. Adjacent angles forming a straight line also sum to 180 degrees. Use the relationship that matches the diagram rather than adding every visible angle.

មុំក្នុងត្រីកោណលើប្លង់មានផលបូក 180 ដឺក្រេ។ មុំជាប់គ្នាលើបន្ទាត់ត្រង់ក៏សរុប 180 ដឺក្រេ។ ត្រូវសម្គាល់មុំក្នុងគំនូរឱ្យត្រូវមុនគណនា។

Formulas

Triangle angle sum

\[A+B+C=180^\circ\]

Adjacent angles on a straight line

\[x+y=180^\circ\]

Symbols and units

Symbol	Meaning	Unit or restriction
A, B, C	Interior triangle angles	Degrees (°)
x, y	Adjacent angles forming a straight line	Degrees (°)

Conditions and limits

• The triangle rule here assumes ordinary flat Euclidean geometry.
• The straight-line rule requires adjacent angles whose outer rays form a line.
• កុំច្រឡំមុំក្នុង និងមុំក្រៅ។

Worked examples

A missing triangle angle

Two interior angles are 50° and 60°.

1. Use \(C=180^\circ-50^\circ-60^\circ\).
2. Calculate \(C=70^\circ\).

70°

ដកមុំដែលស្គាល់ពី 180 ដឺក្រេ។

A straight-line partner

One of two adjacent straight-line angles is 125°.

1. Use \(y=180^\circ-125^\circ\).
2. Calculate \(y=55^\circ\).

55°

មុំទាំងពីរបំពេញបន្ទាត់ត្រង់ ដូច្នេះសរុប 180 ដឺក្រេ។

Common mistakes

Instead of	Use	Why
Triangle angles sum to 360°.	Triangle interior angles sum to 180°.	360° is a full turn, not the interior sum of a triangle.
Every pair of adjacent angles adds to 180°.	Only a straight-line pair necessarily adds to 180°.	Adjacency alone is not enough.

Practice

Solve these before revealing the worked solutions. Include units where relevant.

សាកល្បងដោះស្រាយមុនបើកមើលចម្លើយ។ សូមបង្ហាញជំហាន និងឯកតាដែលពាក់ព័ន្ធ។

1. A triangle has angles 40° and 80°. Find the third.
2. Find the straight-line partner of 35°.
3. Can 90°, 60°, and 40° be the angles of one flat triangle?

Answers and steps

Show solutions / បង្ហាញដំណោះស្រាយ

1. 60°

   180 − 40 − 80 = 60.

2. 145°

   180 − 35 = 145.

3. No.

   Their sum is 190°, not 180°.

Quick recap

• Match the rule to the geometry.
• Triangle interior angles sum to 180°.
• Include the degree unit.