Question

test practice

1. multiple choice a home plate from a baseball field is modeled by the diagram.

what is the value of x in degrees? (lesson 7-1)
a. 45
b. 90
c. 120
d. 180

1. open response find the measure of ∠rkl.

(lesson 7-1)
$\angle l=(3x + 2)^\circ$

Explanation:

Step1: Identify polygon type & sum

The shape is a pentagon. The sum of interior angles of an n-sided polygon is $(n-2)\times180^\circ$. For $n=5$:
$$(5-2)\times180^\circ = 540^\circ$$

Step2: Sum known angle values

There are two right angles ($90^\circ$ each):
$$90^\circ + 90^\circ = 180^\circ$$

Step3: Set up equation for x

The remaining 3 angles are $x^\circ$ each. Total sum equals $540^\circ$:
$$3x + 180 = 540$$

Step4: Solve for x

Subtract 180, then divide by 3:
$$3x = 540 - 180 = 360$$
$$x = \frac{360}{3} = 120$$

Answer:

C. 120