# ACT Practice Math Questions: Working with Angles

A big part of geometry involves working with angles, so it shouldn’t be a surprise that the ACT Math exam contains a number of questions involving them. You may want to brush up on the properties of angles before you take on the following practice questions (and definitely before you tackle the ACT!)

## Practice questions

- In the figure,
*A*,*B*, and*C*are collinear.The measure of angle

*ABD*is 4 times that of angle*DBC*. What is the measure of angle*ABD*?**A.**36 degrees

**B.**45 degrees

**C.**72 degrees

**D.**108 degrees

**E.**144 degrees - The next figure shows three straight lines that intersect at point
*M*. If angle*EMF*measures 47 degrees and angle*AMB*measures 29 degrees, what is the degree measure of angle*CME*?

**A.**72 degrees

**B.**76 degrees

**C.**104 degrees

**D.**133 degrees

**E.**151 degrees

## Answers and explanations

- The correct answer is Choice
**(E).**Because the value of angle

*ABD*measures 4 times that of angle*DBC*, angle*ABD*= 4*x*and angle*DBC*=*x*. Because*A*,*B*, and*C*are collinear, the sum of angle*DBC*and angle*ABD*is 180 degrees. To find the measure of angle*ABD*, set up an equation and solve for*x*:Don’t stop there and pick Choice (A), though. The value of

*x*is the measure of angle*DBC*. Multiply 36 by 4 to get 144 degrees, which is 4*x*and the measure of angle*ABD*. - The correct answer is Choice
**(D).**

Scan the figure to determine which angles are equal. Angle*AMB*and angle*DME*are vertical angles, so they’re equal. Angle*DME*also measures 29 degrees. The same goes for angle*EMF*and angle*BMC*. They’re equal, so angle*BMC*also measures 47 degrees. The remaining two angles, angle*CMD*and angle*AMF*, are also vertical angles and equal. The degree measures of the 6 angles in the figure total to 360 degrees because they circle around the center point*M*. Create an equation to solve for the degree measure of the remaining two angles:Hang on, though. This is the degree measure of angle

*CMD*, but the question asks for the measure of angle*CME*. You need to add 29 degrees to 104 degrees for a degree measure of angle*CME*, which equals 133 degrees.