Math / Geometry

QuestionThe measures of the angles of a triangle are shown in the figure below. Solve for x .

Studdy Solution

STEP 1

1. We are given a right triangle.
2. One angle is $33^\circ$ .
3. Another angle is $(3x + 9)^\circ$ .
4. The sum of the angles in a triangle is $180^\circ$ .

STEP 2

1. Use the property of the sum of angles in a triangle to set up an equation.
2. Solve the equation for $x$ .

STEP 3

In any triangle, the sum of the interior angles is $180^\circ$ . Since this is a right triangle, one angle is $90^\circ$ . The other two angles are given as $33^\circ$ and $(3x + 9)^\circ$ .

STEP 4

Set up the equation based on the sum of the angles:
$90^\circ + 33^\circ + (3x + 9)^\circ = 180^\circ$

STEP 5

Simplify the equation:
$123^\circ + (3x + 9)^\circ = 180^\circ$

STEP 6

Combine like terms:
$123^\circ + 3x + 9^\circ = 180^\circ$ $132^\circ + 3x = 180^\circ$

STEP 7

Isolate the term with $x$ :
$3x = 180^\circ - 132^\circ$ $3x = 48^\circ$

STEP 8

Solve for $x$ by dividing both sides by 3:
$x = \frac{48^\circ}{3}$ $x = 16^\circ$
The value of $x$ is:
$\boxed{16^\circ}$

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