Answer:
The value of BEF = 36°
Step-by-step explanation:
Given:
Angle AED = 90°
Angle BEF = 3x°
Angle CEF = 54°
Find;
The value of BEF
Computation:
We know that;
Angle AED = Angle BEC (Vertical opposite angle)
So,
Angle AED = Angle Angle BEF + Angle CEF
90 = 3x + 54
3x = 90 - 54
3x = 36
x = 36 / 3
x = 12
The value of BEF = 3x
The value of BEF = 3(12)
The value of BEF = 36°
<span>When your income is more than your expenses, y</span>ou have surplus
The present age of mother and her daughter respectively are; 40 and 10 years respectively.
<h3>How to Solve Algebra Word Problems?</h3>
Let x and y be the present age of mother and her daughter respectively.
Therefore;
x + y = 50
x = 50 − y .....(1)
After 20 years, mother's age will be twice her daughter's age at the time. Thus;
x + 20 = 2(y + 20)
x − 2y = 20 .....(2)
Plugging eq 1 into eq 2 gives us;
50 − y − 2y = 20
3y = 30
y = 10
Thus;
x = 50 − 10
x = 40
Thus, the present age of mother and her daughter is 40 and 10 years respectively.
Translation of the question into English is;
The sum of the present ages of mother and her daughter is 50 years. After 20 years, mother's age will be twice her daughter's age at the time. Find their present ages.
Read more about Algebra Word Problems at; brainly.com/question/21405634
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Answer:
ABCD is a parallelogram.
Step-by-step explanation:
A parallelogram is a quadrilateral that has two parallel and equal pairs of opposite sides.
From the given diagram,
Given: AD = BC and AD || BC, then:
i. AB = DC (both pairs of opposite sides of a parallelogram are congruent)
ii. <ADC = < BCD and < DAB = < CBA
thus, AD || BC and AB || DC (both pairs of opposite sides of a parallelogram are parallel)
iii. < BAC = < DCA (alternate angle property)
iv. Join BD, line AC and BC are the diagonals of the quadrilateral which bisect each other. The two diagonals are at a right angle to each other.
v. <ADC + < BCD + < DAB + < CBA = 
(sum of angles in a quadrilateral equals 4 right angles)
Therefore, ABCD is a parallelogram.
Answer:
9
Step-by-step explanation: 3x4= 12 -3=9
