Lesson 2Solve for Unknown Angles using Equations

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

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.

< r is adjacent to < s

< r is supplementary to < 25

< r is vertical to < t

Plus many more….

Lesson Summary:To solve problems involving angles, I must follow these steps:1)Identify the angle relationship2)Set up an equation3)Solve for the unknown value4)Check answer by substitution

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.

Solution

A supplementary angle is created with 28°, 16° and p°= 180°

Equation: 28+16+p=180 44+p=180 p=136

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.

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°

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.

Solution

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=xNow, we must find the measurement of t which 180-64=116The measurement of angle t=116°

x°

Solving Angle Steps:To solve problems involving angles, I must follow these steps:1)Identify the angle relationship2)Set up an equation3)Solve for the unknown value4)Check answer by substitution