If EF bisects angle CEB, angle CEF=7x + 21 and angle FEB = 10x - 3, find the measure of DEB.
1 answer:
Answer: DEb = 26°
Step-by-step explanation:
<u>Given information</u>
CEF = 7x + 21
FEB = 10x - 3
<u>Given expression deducted from the definition of the bisector</u>
FEB = CEF
<u>Substitute values into the expression</u>
10x - 3 = 7x + 21
<u>Subtract 7x on both sides</u>
10x - 3 - 7x = 7x + 21 - 7x
3x - 3 = 21
<u>Add 3 on both sides</u>
3x - 3 + 3 = 21 + 3
3x = 24
<u>Divide 3 on both sides</u>
3x / 3 = 24 / 3
x = 8
<u>Find the sum of the angle of CEF and FEB</u>
7x + 21 + 10x - 3
=7 (8) + 21 + 10 (8) - 3
=56 + 21 + 80 - 3
=77 + 80 - 3
=157 - 3
=154
<u>Subtract 154 from the straight angle</u>
DEB = 180 - 154
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The area and perimeter of the triangle is 2/5 square units and (2√10 + 4√5) / 5 units
<h3>Perimeter and area of the triangle giving the equation of a line</h3>First we will plot the giving lines, determine the point of intersection and then use the Pythagoras theorem to determine the dimension of the right triangle.
From the given equation of the lines, the points of intersection of the line are (x₁, y₁) = (- 0.4, 5.2), (x₂, y₂) = (-0.8, 4.4) and (x₃, y₃) = (0, 4)
For the base
b² = c² -a²
b = √(-0.8)² + (4 - 4.4)²
b = 2√5 / 5
For the height
h = √((- 0.4) - (- 0.8))² + (5.2 - 4.4)²
height = 2√5 / 5
For the hypotenuse
r = √2 · b
r = 2√10 / 5
<h3>Determine the Perimeter and area</h3>Perimeter = s1+s2+s3
Perimeter = 2√5 / 5 + 2√5 / 5 + 2√10 / 5
Perimeter = (2√10 + 4√5) / 5 units
<u>For the area</u>
area = 1/2* base * height
A = 0.5 · (2√5 / 5) · (2√5 / 5)
A = 2/5 square units
Hence the area and perimeter of the triangle is 2/5 square units and (2√10 + 4√5) / 5 units
Learn more on area and perimeter of triangles here: brainly.com/question/21511715
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