Angle Relationships & Equations
Aligned to 7.G.B.5 — Common Core State Standards for Mathematics.
What this lesson teaches
Complementary angles add to 90°; supplementary angles add to 180°. Vertical angles (opposite each other where two lines cross) are equal. Use these facts to write an equation and solve for an unknown angle.
Worked examples
Example 1
Angles A and B are supplementary, with A = 2x and B = x. Then 2x + x = 180, so 3x = 180 and x = 60. Therefore A = 120° and B = 60°.
Example 2
Two vertical angles are always equal. If one is 3x and its vertical partner is 75°, then 3x = 75 and x = 25.
Example 3
Complementary angles sum to 90, supplementary to 180. An angle of 35° has a complement of 55° and a supplement of 145°.
Practice questions
- Two complementary angles measure x and 3x. Find both angles.
- One of two vertical angles measures 47°. What is the other?
- Two angles on a straight line measure 5x and 4x. Solve for x, then find each angle.
Watch the lesson
Every lesson comes with a video taught in English and Spanish — the same video the QR code in the printed workbook opens.
▶ Watch this lessonEn español
Relaciones entre Ángulos y Ecuaciones
Los ángulos complementarios suman 90°; los suplementarios suman 180°. Los ángulos opuestos por el vértice (donde se cruzan dos rectas) son iguales. Usa estos hechos para plantear una ecuación y hallar un ángulo desconocido.
Ejemplo 1: Los ángulos A y B son suplementarios, con A = 2x y B = x. Entonces 2x + x = 180, así que 3x = 180 y x = 60. Por lo tanto A = 120° y B = 60°.
Ejemplo 2: Dos ángulos opuestos por el vértice siempre son iguales. Si uno es 3x y su opuesto es 75°, entonces 3x = 75 y x = 25.
Ejemplo 3: Los ángulos complementarios suman 90 y los suplementarios 180. Un ángulo de 35° tiene complemento 55° y suplemento 145°.
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