Answer:
Yes, we can conclude that Triangle ABC is similar to triangle DEF because the measures of the 3 angles of both triangles are congruent.
Step-by-step explanation:
We have the measure of 2 angles from both triangles, and we know that triangles have 180°, so we can solve for the measure of the third angle for both triangles.
Triangle ABC:
Measure of angle A= 60°
Measure of angle C= 40°
Measure of angle B = 180°- (measure of angle A + measure of angle C) = 180° - (60° + 40°) = 80°
Triangle DEF
Measure of angle E= 80°
Measure of angle F= 40°
Measure of angle D= 180° - (measure of angle E + measure of angle F) = 180° - (80° + 40°) = 60°
The measures of the angles in Triangle ABC are: 60°, 40°, and 80°.
The measures of the angles in Triangle DEF are: 60°, 40°, and 80°.
Since the measure of 3 angles of the two triangles are the same, we know that the two triangles are similar.
The required number is -3 which when added to the numerator and to the denominator of 5/8 results in a fraction whose value is 0.4.
<h3>What is a fraction?</h3>
Fraction is the ratio of a particular part to the whole parts of an object. A fraction has a numerator and a denominator.
<h3>Calculation:</h3>
The given fraction is 5/8
Consider a number as 'x' which is added to both the numerator and the denominator of the given fraction.
So,
(5 + x)/(8 + x)
Since it is given that the result is 0.4 i.e., 4/10, we can write
(5 + x)/(8 + x) = 4/10
⇒ 10(5 + x) = 4(8 + x)
⇒ 50 + 10x = 32 + 4x
⇒ 10x - 4x = 32 - 50
⇒ 6x = -18
⇒ x = -18/6
∴ x = -3
Therefore, the required number is -3.
Check:
(5 + (-3))/(8 + (-3)) = (5 - 3)/(8 - 3) = 2/5 = 0.4
Learn more about fractions here:
brainly.com/question/17220365
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4 because 4 x 4 =16 and 4+4=8
Where is it shown? Please show a picture
Answer:
StartFraction pi Over 3 EndFraction
Step-by-step explanation:
we know that
The circumference of a circle subtends a central angle of 360 degrees or 2π radians
so
by proportion
Find out the central angle for an arc equal to One-sixth of the circumference of a circle
Let
x -----> the measure of the central angle in radians for an arc equal to One-sixth of the circumference
Simplify
therefore
StartFraction pi Over 3 EndFraction
