Question

1. if m∠9 = 124°, then m∠8
2. if m∠7 = 47°, then m∠9 =
3. if m∠8 = 158°, then m∠9
4. if m∠7 = 15°, then m∠6 =

in exercises 13–16, assume ∠ and ∠c are supplementary.

1. if m∠a = 42°, then m∠b =
2. if m∠b = 78°, then m∠a =
3. if m∠a = 17°, then m∠b =
4. if m∠b = 45°, then m∠a =

find the value of the variable.

1. diagram of two intersecting lines with 110° and (2x + 40)°

Explanation:

Problem 9:

Step1: Identify angle relationship (supplementary)

$\angle 8$ and $\angle 9$ are supplementary (form a linear pair), so $m\angle 8 + m\angle 9 = 180^\circ$.

Step2: Substitute and solve

Given $m\angle 9 = 124^\circ$, then $m\angle 8 = 180^\circ - 124^\circ = 56^\circ$.

Step1: Identify angle relationship (vertical or supplementary? Assuming $\angle 7$ and $\angle 9$ are supplementary or vertical. Wait, likely $\angle 7$ and $\angle 9$: if $\angle 7$ and $\angle 8$ are supplementary, and $\angle 8$ and $\angle 9$ are supplementary, then $\angle 7$ and $\angle 9$ are equal? Wait, no, maybe $\angle 7$ and $\angle 9$ are supplementary? Wait, no, let's re - think. If $\angle 7$ and $\angle 8$ are adjacent (linear pair), and $\angle 8$ and $\angle 9$ are adjacent (linear pair), then $\angle 7$ and $\angle 9$ are equal? Wait, no, if $\angle 7$ and $\angle 8$ are supplementary ($m\angle 7 + m\angle 8 = 180^\circ$) and $\angle 8$ and $\angle 9$ are supplementary ($m\angle 8 + m\angle 9 = 180^\circ$), then $m\angle 7 = m\angle 9$? Wait, no, that would be if they are vertical angles. Wait, maybe the diagram shows that $\angle 7$ and $\angle 9$ are vertical angles? No, maybe $\angle 7$ and $\angle 9$ are supplementary. Wait, the problem says "If $m\angle 7 = 47^\circ$, then $m\angle 9$". Let's assume that $\angle 7$ and $\angle 9$ are supplementary (linear pair with a common angle). Wait, no, maybe $\angle 7$ and $\angle 9$ are supplementary. So $m\angle 7 + m\angle 9 = 180^\circ$. Then $m\angle 9 = 180^\circ - 47^\circ = 133^\circ$.

Step2: Calculate

$m\angle 9=180 - 47=133^\circ$

Step1: Angle relationship (supplementary)

$\angle 8$ and $\angle 9$ are supplementary, so $m\angle 8 + m\angle 9 = 180^\circ$.

Step2: Substitute and solve

Given $m\angle 8 = 158^\circ$, then $m\angle 9 = 180^\circ - 158^\circ = 22^\circ$.

Answer:

$56^\circ$

Problem 10: