Bob J.

asked • 10/27/20# If the measure of angle ABC is one degree less than three times the measure of angle ABD and the measure of angle DBC = 47, find each measure

This is for school and i dont understand it at all. Please give the work and answers

## 2 Answers By Expert Tutors

Cecilia M. answered • 10/27/20

Experienced Teacher Specializing in Mathematics for ages 3 - 50+

**If the measure of angle ABC is one degree less than three times the measure of angle ABD **

an equation for that is

measurement of angle ABC = 3(measurement of angle ABD) - 1

If angle ABC and angle ABD are inside of angle DBC then

The measurements of angle ABC and angle ABD added together is 47 degrees.

The measurement of angle DBC = 47°

therefore

The measurement of angle ABC + the measurement of angle ABD = 47°

m∠ABC = 3(m∠ABD) - 1

m∠ABC + m∠ABD = 47

3(m∠ABD) - 1 + m∠ABD = 47

4(m∠ABD) + 1 - 1 = 47 - 1

4(m∠ABD) = 46

4(m∠ABD) / 4 = 46 / 4

m∠ABD = 11.5°

m∠ABC = 3(m∠ABD) - 1

m∠ABC = 3(11.5) - 1

m∠ABC = 34.5 - 1

m∠ABC = 33.5

Hi. It is a triangle ABC with a line BD inside the triangle, from the vertex to the base. Angle ABD would be x, while angle ABC is 3x-1. Also, angle DBC is 47 degrees. Draw the triangle, and label the points and angles, so you can see why the equation I will write makes sense. In this case, x + 47 = 3x - 1. If you solve for x, you will get x = 24. Therefore, angle ABD is 24 degrees, and angle ABC is 3x-1 = 71 degrees.

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Mark M.

The relative location of the angles is needed before any solution can be given.10/27/20