1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Vikki [24]
2 years ago
15

The figure shows a rectangle ABCD where the diagonals AC and BD intersect at E.

Mathematics
2 answers:
sesenic [268]2 years ago
5 0

Answer:

(i) 64°

(ii) 26°

Step-by-step explanation:

Ostrovityanka [42]2 years ago
5 0

Answer:

(i) m<ADB = 64°

(ii) m<ACD = 26°

Step-by-step explanation:

I use this to mean the measure of angle ADC: m<ADC

(i)

m<BEC = 52°

<DEA and <BEC are vertical angles, so they are congruent.

m<DEA = m<BEC = 52°

Polygon ABCD is a rectangle. When the diagonals, AC and BD, of a rectangle are drawn, 4 triangles are formed. Each two opposite triangles are congruent, and all 4 triangles are isosceles.

Triangle ADE is an isosceles triangle with congruent sides ED and EA. That makes opposite angles ADB and DAC congruent. Also the sum of the measures of the angles of a triangle is 180°.

m<ADB + m<DAC + m<DEA = 180°

m<ADB = m<DAC; m<DEA = 52°

2m<ADB + 52° = 180°

2m<ADB = 128°

m<ADB = 64°

(ii)

Angles DEC and BEC form a linear pair. That means the angles are supplementary, and the sum of their measures is 180°.

m<DEC + m<BEC = 180°

m<DEC + 52° = 180°

m<DEC = 128°

Triangle DEC is an isosceles triangle with congruent sides ED and EC. That makes opposite angles ACD and BDC congruent.

m<ACD + m<BDC + m<DEC = 180°

2m<ACD + 128° = 180°

2m<ACD = 52°

m<ACD = 26°

You might be interested in
Which of the following is the equation of
Neporo4naja [7]

Answer:

a) Option A is correct.

b) Option C is correct.

Step-by-step explanation:

a) Which of the following is the equation of  the line passing through the points (1, 1)  and (-3,5)?

We will use the equation

(y-y₁)=m(x-x₁)

m= (y₂-y₁)/(x₂-x₁)

m= (5-1)/(-3-1)

m= 4/-4

m= -1

Consider point (1,1) and Putting value of m

(y-y₁)=m(x-x₁)

(y-1)=1(x-1)

y-1=x-1

y=x-1+1

y=x

So, Option A is correct.

b) Which of the following is the equation of a  line with a slope of 0 passing through (2,5)?

The formula used is:

y= mx+b

Finding b:

5=0(2)+b

=> b = 5

So, equation is:

y = mx+b

y=0x+5

y=5

So, Option C is correct.

5 0
3 years ago
If a man hold his breath for three minutes and dies because of it what is that called
miss Akunina [59]

Answer:

Holding your breath is called static Apnea and a common person can't hold their breath for long. If a person holds their breath for long and dies because of it, it may be called lack of breath or lack of respiration.

6 0
3 years ago
Helpppp plsss!!!!!!
Vanyuwa [196]
A because -1/4x is your slope and the +5 would just be shifted over to the 5 on the y-axis
5 0
2 years ago
Read 2 more answers
Is 0.252 a whole number?
NemiM [27]

Answer:

No, that is a decimal

Step-by-step explanation:

A whole number is like 1.

1.5 wouldn't be a whole number.

A whole number is a positive integer or 0

3 0
3 years ago
Read 2 more answers
What is the least common denominator of 3/20 and 8/15?<br> A.30 <br> B.20<br> C.5<br> D.60
Sidana [21]
5 since both numbers are divisible by 5 and not by any smaller number

6 0
3 years ago
Read 2 more answers
Other questions:
  • Josh earned $80 to use for back-to-school shopping. So far he has spent $24 on a backpack and $32 on new shoes. Think abt the yo
    11·1 answer
  • What is 12.9 rounded to 1 decimal place
    11·1 answer
  • CAN SOMEONE PLEASE HELP ME????
    6·1 answer
  • A square has the side measurement of s=6^3/2 , Use the formula A = s^2 , find the area of the square
    15·1 answer
  • -7 exponent 2 - x + 6x + x exponent 2
    8·2 answers
  • Which term best describes the relationship between time and number of labels printed?
    13·1 answer
  • What is Evaluate 3+jk+^3 when j=2 and k=6
    13·1 answer
  • Twenty times one hundred and one (20 x 101)
    11·1 answer
  • Find the value of x please help<br>Will give brainliest​
    15·1 answer
  • HELP GUYS ASAP THIS QUESTION IS DUE SOLVE
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!