Lesson 13

Using Equations to Solve for Unknown Angles

Let’s figure out missing angles using equations.

Problem 1

Segments \(AB\), \(DC\), and \(EC\) intersect at point \(C\). Angle \(DCE\) measures \(148^\circ\). Find the value of \(x\).

Point C lies on segment A, B. Segments D C and E C are on the same side of A, B and form 3 angles.  Angle A, C D measures x degrees, Angle D C E measures 148 degrees. Angle B C E measures x degrees.

Problem 2

Line \(\ell\) is perpendicular to line \(m\). Find the value of \(x\) and \(w\).

Three angles between line l and line m are 19 degrees, x degrees, w degrees. The angles marked w degrees and 128 degrees are adjacent anf form a straight line.

Problem 3

If you knew that two angles were complementary and were given the measure of one of those angles, would you be able to find the measure of the other angle? Explain your reasoning.

Problem 4

Here is a polygon on a grid.

A polygon aligned to a square grid.
  1. Draw a scaled copy of the polygon using a scale factor 3. Label the copy A.

  2. Draw a scaled copy of the polygon with a scale factor \(\frac{1}{2}\). Label it B.

  3. Is Polygon A a scaled copy of Polygon B? If so, what is the scale factor that takes B to A?

(From Unit 2, Lesson 2.)

Problem 5

Jada, Elena, and Lin walked a total of 37 miles last week. Jada walked 4 more miles than Elena, and Lin walked 2 more miles than Jada. The diagram represents this situation:

Three tape diagrams. Elena, 1 part, m. Jada 2 parts, m, 4, Lin, 3 parts, m, 4, 2. Bracket indicates the total of all 3 diagrams is 37.


Find the number of miles that they each walked. Explain or show your reasoning.

(From Unit 3, Lesson 12.)