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Angle Equations: Solve Unknown Angles with Diagrams

Learn to solve for unknown angles using equations in diagrams involving complementary, supplementary, vertical, and adjacent angles. Follow steps to identify angle relationships, set up and solve equations, and check answers. Practice finding values in various angle scenarios.

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Angle Equations: Solve Unknown Angles with Diagrams

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  1. Lesson 2 Solve for Unknown Angles using Equations

  2. Lesson Objective: I will solve for unknown angles in word problems and in diagrams involving complementary, supplementary, vertical, and adjacent angles.

  3. Two lines meet at a point. In a complete sentence, describe the relevant angle relationships in the diagram. Find the values of r, s, and t.

  4. < r is adjacent to < s < r is supplementary to < 25 < r is vertical to < t Plus many more….

  5. Lesson Summary: To solve problems involving angles, I must follow these steps: Identify the angle relationship Set up an equation Solve for the unknown value Check answer by substitution

  6. Two lines meet at the vertex of a ray. In a complete sentence, describe the relevant angle relationships in the diagram. Set up and solve an equation to find the value of p and r.

  7. Solution • A supplementary angle is created with 28°, 16° and p°= 180° • Equation: 28+16+p=180 44+p=180 p=136

  8. Three lines meet at a point. In a complete sentence, describe the relevant angle relationships in the diagram. Set up and solve an equation to find the value of z.

  9. Solution • Angle z and an angle = 90° which is a complementary angle • The unknown angle is 19° because it is an opposite vertical angle to a known measured angle. • Thus, 90-19=z • 71=z • The angle measurement of z=71°

  10. Two lines meet at the vertex of a ray. The ray is perpendicular to one of the lines as shown. In a complete sentence, describe the relevant angle relationships in the diagram. Set up and solve an equation to find the value of t.

  11. The angles are supplementary which means the total of all angles will = 180° • From the diagram, we can see that one angle is 90° and one angle is 26° • Thus our equation is 180=90+26+x • Solve for our variable 180=116+x 64=x Now, we must find the measurement of t which 180-64=116 The measurement of angle t=116° Solution x°

  12. Solving Angle Steps: To solve problems involving angles, I must follow these steps: Identify the angle relationship Set up an equation Solve for the unknown value Check answer by substitution

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