Question

solve for x.
5.
6.
x =
x =

1. use the diagram at the right.

a. which angle is the exterior angle?
circle the correct answer.
138° 58° x°
b. which two angles are the remote interior angles? circle two answers.
138° 58° x°
c. should you subtract or add 138 and 58 to find the value of x? shade the correct answer.
subtract add
d. solve for x.

1. label the diagram at the right using the following information:

• a 150° exterior angle
• one 85° remote interior angle
• one 65° remote interior angle

florida edgems math - course 3
copyright ©2022 all rights reserved.
lesson 7.3 - angle relationships in triangles

Explanation:

Problem 5

Step1: Sum angles to 180°

$25 + 6x + (5x+1) = 180$

Step2: Simplify left side

$26 + 11x = 180$

Step3: Isolate variable term

$11x = 180 - 26$
$11x = 154$

Step4: Solve for x

$x = \frac{154}{11}$

Step1: Sum angles to 180°

$x + x + (x-30) = 180$

Step2: Simplify left side

$3x - 30 = 180$

Step3: Isolate variable term

$3x = 180 + 30$
$3x = 210$

Step4: Solve for x

$x = \frac{210}{3}$

a. An exterior angle is formed outside a triangle by extending a side, so $138^\circ$ is the exterior angle.
b. Remote interior angles are the two angles inside the triangle not adjacent to the exterior angle, so $58^\circ$ and $x^\circ$ are the remote interior angles.
c. The exterior angle theorem states exterior angle = sum of remote interior angles, so subtract 58 from 138 to find $x$.
d. Use the exterior angle theorem: $138 = 58 + x$, solve for $x$.

Answer:

$x = 14$

---

Problem 6