Math / Geometry

QuestionDetermine the value of x. $147^\circ$ $x + 42^\circ$ $2x$

Studdy Solution

STEP 1

What is this asking? We need to find the value of $x$ in a triangle with angles $x + 42$ degrees and $2x$ degrees, given an exterior angle of $147$ degrees. Watch out! Don't forget that the sum of the angles in a triangle is $180$ degrees, and remember the relationship between exterior and interior angles!

STEP 2

1. Find the third interior angle.
2. Set up an equation using the triangle angle sum.
3. Solve for $x$ .

STEP 3

An exterior angle of a triangle is equal to the sum of the two non-adjacent interior angles.
Our exterior angle is $147$ degrees.

STEP 4

Let's call the third interior angle $a$ .
We know that $147^\circ = a + 2x^\circ$ , so $a = 147^\circ - 2x^\circ$ .

STEP 5

So, we can write the equation: $(x + 42)^\circ + (2x)^\circ + (147 - 2x)^\circ = 180^\circ$ .

STEP 6

We have $x + 42 + 2x + 147 - 2x = 180$ .
Combining like terms, we get $x + 189 = 180$ .

STEP 7

Subtract $189$ from both sides of the equation: $x + 189 - 189 = 180 - 189$ .
This gives us $x = -9$ .

STEP 8

The value of $x$ is $-9$ .

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