Question

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1. levi was designing a kite. he needs to determine the measure of $angle a$ before cutting the fabric. what is the measure of angle a?

1. jess was drawing a map of her neighborhood. what is the measure of the angle of the intersection between derby drive and rosemont?

Explanation:

Step1: Solve for x (Problem 9)

The angles form a straight line ($180^\circ$):
$$(6x + 4) + (4x + 26) + 110 = 180$$
Simplify:
$$10x + 140 = 180$$
$$10x = 40$$
$$x = 4$$

Step2: Find $\angle A$ (Problem 9)

$\angle A$ is the difference between the two lower angles:
$$\angle A = (4x + 26) - (6x + 4)$$
Substitute $x=4$:
$$\angle A = (4(4)+26) - (6(4)+4) = 42 - 28 = 14$$

Step3: Solve for x (Problem 10)

Angles around a point sum to $360^\circ$:
$$(3x + 15) + 103 + (x + 10) = 360$$
Simplify:
$$4x + 128 = 360$$
$$4x = 232$$
$$x = 58$$

Step4: Find the intersection angle (Problem10)

Substitute $x=58$ into $(x + 10)$:
$$x + 10 = 58 + 10 = 68$$

Answer:

1. The measure of $\angle A$ is $14^\circ$
2. The measure of the intersection angle is $68^\circ$