Math / Geometry

Question\#2. a) What is the angle-pair relationship between the labeled angles? b) Use the relationship to write an equation and solve for $x$ .

Studdy Solution

STEP 1

1. The given diagram has intersecting lines forming vertical angles and adjacent angles.
2. Adjacent angles formed by intersecting lines are supplementary, meaning their measures add up to $180^\circ$ .
3. The labeled angles are $102^\circ$ and $x + 15^\circ$ , which are adjacent.

STEP 2

1. Identify the relationship between the labeled angles.
2. Write an equation based on the relationship.
3. Solve the equation for $x$ .

STEP 3

Identify the relationship between the labeled angles. Since the angles are adjacent and formed by intersecting lines, they are supplementary.

STEP 4

Write the equation based on the supplementary relationship. The sum of the angles is $180^\circ$ .
$102^\circ + (x + 15^\circ) = 180^\circ$

STEP 5

Simplify the equation to solve for $x$ .
$102^\circ + x + 15^\circ = 180^\circ$ $x + 117^\circ = 180^\circ$ $x = 180^\circ - 117^\circ$ $x = 63^\circ$
Solution: The value of $x$ is $63^\circ$ .

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