QuestionFind angles $\angle 1$ and $\angle 2$ where $\angle 2$ is a supplement and $36^{\circ}$ more than $2 \times \angle 1$ .

Studdy Solution

STEP 1

Assumptions1. $\angle$ is the supplement of $\angle1$ . $\angle$ is $36^{\circ}$ more than two times $\angle1$

STEP 2

First, we need to understand what it means for two angles to be supplementary. Two angles are supplementary if the sum of their measures is $180^{\circ}$ . This gives us our first equation $\angle1 + \angle2 =180^{\circ}$

STEP 3

Next, we need to translate the second statement into an equation. $\angle2$ is $36^{\circ}$ more than two times $\angle1$ can be written as $\angle2 =2\angle1 +36^{\circ}$

STEP 4

Now we have a system of two equations. We can solve this system by substitution or elimination. In this case, substitution is easier. We can substitute the expression for $\angle2$ from the second equation into the first equation $\angle1 + (2\angle1 +36^{\circ}) =180^{\circ}$

STEP 5

implify the equation by combining like terms $3\angle1 +36^{\circ} =180^{\circ}$

STEP 6

Subtract $36^{\circ}$ from both sides of the equation to isolate the term with $\angle1$ $3\angle1 =180^{\circ} -36^{\circ}$

STEP 7

Calculate the right side of the equation $3\angle1 =144^{\circ}$

STEP 8

Divide both sides of the equation by3 to solve for $\angle1$ $\angle1 =144^{\circ} /3$

STEP 9

Calculate the value of $\angle$ $\angle =48^{\circ}$

STEP 10

Now that we have the measure of $\angle$ , we can find the measure of $\angle2$ by substituting $\angle$ into the second equation $\angle2 =2\angle +36^{\circ}$

STEP 11

Substitute the value of $\angle$ into the equation $\angle =(48^{\circ}) +36^{\circ}$

STEP 12

Calculate the value of $\angle2$ $\angle2 =96^{\circ} +36^{\circ} =132^{\circ}$ So, the measure of $\angle$ is $48^{\circ}$ and the measure of $\angle2$ is $132^{\circ}$ .

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