Identify the like terms.

Given: ABCD is a trapezoid, AB=CD, MN is a midsegment, MN=30, BC=17, AB=26 Find: m∠A, m∠B, m∠C, and m∠D

enyata [817]

Answer:

The measures of angle ∠A, ∠B, ∠C, and ∠D are 60, 120, 120 and 60 degree respectively.

Step-by-step explanation:

Given information:AB=CD, MN is a midsegment, MN=30, BC=17, AB=26

Since two opposites sides are equal, therefore we can say that two no parallel sides are equal.

The length of midsegment is average of length of parallel lines.

$MN=\frac{AD+BC}{2}$

$30=\frac{AD+17}{2}$

$60=AD+17$

$43=AD$

Draw perpendiculars on AD from B and C. Let angle A be θ. D

$AD=AE+EF+FD$

Since ABCD is an isosceles trapezoid, therefore AE=FD and EF=BC

$AD=AE+EF+AE$

$43=2(AE)+17$

$26=2(AE)$

$13=AE$

$\cos\theta=\frac{base}{hypotenuse}$

$\cos\theta=\frac{AE}{AB}$

$\cos\theta=\frac{13}{26}$

$\cos\theta=\frac{1}{2}$

$\theta=\cos^{-1}\frac{1}{2}$

$\theta=60$

Since ABCD is an isosceles trapezoid, therefore angles A and D are same. Angle B and C are same.

$\angle A=\angle D=60^{\circ}$

The sum of two consecutive angles of a trapezoid is 180 degree by consecutive interior angle theorem.

$\angle A+\angle B=180^{\circ}$

$60^{\circ}+\angle B=180^{\circ}$

$\angle B=120^{\circ}$

$\angle B=\angle C=120^{\circ}$

Therefore measures of angle ∠A, ∠B, ∠C, and ∠D are 60, 120, 120 and 60 degree respectively.

3 0

3 years ago

Dr. Lawrence is the director of Counseling Services at her university. She is planning to conduct a survey of 100 students at th

Tanzania [10]

Answer:

The type of sampling method Dr. Lawrence going to use is Quota Sampling.

Step-by-step explanation:

In quota sampling participants are chosen nonrandomly so it is not a representative sampling method. In this case Dr.Lawrence has a quota of 15% for first-time students and 85% for returning, so the survey she is conducting is non-random. The sampling method she should use is Quota Sampling.

4 0

2 years ago

The triangles below are simular. which statement about the triangles is true?

PilotLPTM [1.2K]

Answer:

C

Step-by-step explanation:

8 0

2 years ago

Find the volume of the figure. If necessary, round the answer to the nearest whole number.

lisabon 2012 [21]

Answer:

V = 108 ft³

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

Left to Right

Geometry

Volume of a Rectangular Prism Formula: V = lwh

l is length
w is width
h is height

Step-by-step explanation:

Step 1: Define

Identify variables

l = 4 ft

w = 3 ft

h = 9 ft

Step 2: Find Volume

Substitute in variables [Volume of a Rectangular Prism Formula]: V = (4 ft)(3 ft)(9 ft)
Evaluate [Order of Operations]: V = 108 ft³

6 0

3 years ago

What is 100% of 94 in a decimal

oee [108]

Answer:

94

Step-by-step explanation:

100 percent of something is always that number.

Hope this helps Buddy!

- Courtney

6 0

3 years ago