Question

linear pair angles are adjacent and supplementary.
2 find m∠rqt.
image of intersecting lines with angles (4x + 15)° and (10x - 3)° at point q
a) 59° disappointed
b) 61° exhausted
c) 63° shocked
d) 117° outraged
e) 119° overwhelmed

Explanation:

Step1: Identify linear pair relationship

Angles $(4x+15)^\circ$ and $(10x-3)^\circ$ are a linear pair, so their sum is $180^\circ$.
$$(4x + 15) + (10x - 3) = 180$$

Step2: Simplify and solve for $x$

Combine like terms and isolate $x$.
$$14x + 12 = 180$$
$$14x = 168$$
$$x = 12$$

Step3: Calculate $\angle RQT$

$\angle RQT$ is equal to $(4x+15)^\circ$ (vertical angles). Substitute $x=12$.
$$m\angle RQT = 4(12) + 15 = 48 + 15 = 63$$

Answer:

C) $63^\circ$