QuestionFind $m \angle A B D$ if $(8x+5)$ and $(5x-20)$ are a linear pair.

Studdy Solution

STEP 1

Assumptions1. The angles form a linear pair, which means they are adjacent and their non-common sides form a straight line.. The measure of angle $AB$ is given by the expression $(8x+5)$ .
3. The measure of the other angle is given by the expression $(5x-20)$ .

STEP 2

Since the angles form a linear pair, the sum of their measures is $180^{\circ}$ . We can set up the equation $(8x+5) + (5x-20) =180$

STEP 3

implify the equation by combining like terms on the left side.
$13x -15 =180$

STEP 4

Add15 to both sides of the equation to isolate the term with $x$ on one side.
$13x =195$

STEP 5

Divide both sides of the equation by13 to solve for $x$ .
$x = \frac{195}{13}$

STEP 6

Calculate the value of $x$ .
$x =15$

STEP 7

Now that we have the value of $x$ , we can substitute it into the expression for $m \angle ABD$ to find its measure.
$m \angle ABD =x +5$

STEP 8

Substitute $x =15$ into the expression for $m \angle ABD$ .
$m \angle ABD =8(15) +5$

STEP 9

Calculate the measure of $m \angle ABD$ .
$m \angle ABD =120 +5 =125^{\circ}$ So, the measure of angle $AB$ is $125^{\circ}$ .

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