## 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.