Question

In a certain linear pair, one angle

measures three less than twice as much as the other.
Draw the diagram that you would draw to
represent this linear pair.

Answer 1

∠ABD = 61° and ∠DBC =119°

Explanation:

Linear Pair: Two adjacent angles are said to form a linear pair angles , if their non-common arms are two opposite rays.

The sum of adjacent angles is 180°.

Refer the attached figure

Let ∠ABD be x

Since we are given that In a certain linear pair, one angle measures three less than twice as much as the other.

So, ∠DBC = 2x-3

Since ∠ABD and ∠DBC are linear pairs

So, ∠ABD + ∠DBC =180°

`x+2x-3=180^(\circ)`

`3x-3=180^(\circ)`

`3x=183`

`x=(183)/(3)`

`x=61`

So, ∠ABD = 61°

Now ∠DBC = 2x-3 = 2(61) -3 =119°

Hence ∠ABD = 61° and ∠DBC =119°

Refer the attached figure.

Answer 2

A linear pair of angles forms a straight line, so it's another way of saying that they are supplementary or add to 180 degrees. So, one angle is: 2x - 3 where the other one is: "x" Add those 2 together, set the sum equal to 180, and then solve for "x".