Question

Two adjacent angles form a resulting angle with measure 160° . m∠1=3x° and m∠2=(2x+10)° . Solve for x . What are the two unknown angles’ measurements?

Answer 1

An illustration shows three rays extending from a common origin. The angles between them are labeled. The first ray extends vertically upward from the vertex, the second ray is inclined upward from the vertex to the right, and the third ray extends horizontally to the right. The angle between the first and the third rays is marked with a right angle symbol. The angle between the first and the second rays is labeled as left parenthesis x plus 4 right parenthesis degrees. The angle between the second and the third rays is labeled as left parenthesis 3x plus 2 right parenthesis degrees.
What are the two unknown angle measures that form the 90° angle?

Answer 2

The sum of adjacent angles is equal to the resulting angle.
So, we can write the equation:
m∠1 + m∠2 = 160°

Substituting the given values:
3x + (2x + 10) = 160°

Combining like terms:
5x + 10 = 160°

Subtracting 10 from both sides:
5x = 150°

Dividing both sides by 5:
x = 30°

Substituting the value of x back into the expressions for m∠1 and m∠2:
m∠1 = 3x = 3(30°) = 90°
m∠2 = 2x + 10 = 2(30°) + 10 = 70°

So, the two unknown angles have measurements of 90° and 70°.