The measure of each angles are m∠F = 46°, m∠D = 32°, m∠E = 102°.
<h3>What is angle?</h3>
An angle in plane geometry is a shape created by two rays or lines that have a common endpoint. The Latin word "angulus," which means "corner," is where the word "angle" comes from. The common endpoint of two rays is known as the vertex, and the two rays are known as sides of an angle.
The angle that lies in the plane need not be in Euclidean space. Angles are referred to as dihedral angles if they are produced by the intersection of two planes in a space other than Euclidean. The symbol "" is used to represent an angle.
We have given that Δ DEF has
m∠D = m∠F - 14
And
m∠E = 10 + 2(m∠F)
We know that that sum of all angels in a triangle is 180°, So
m∠D + m∠E + m∠F = 180°
Substituting the values we get
(m∠F - 14) + (10 + 2(m∠F)) + m∠F = 180°
m∠F - 14 + 10 + 2m∠F +m∠F
4(m∠F) - 4 = 180
4(m∠F) = 180 + 4
4(m∠F) = 184
(m∠F) = 46°
m∠D = 46° - 14
m∠D = 32°
m∠E = 10 + 2(m∠F)
m∠E = 10 + 2( 46°)
m∠E = 10 + 92°
m∠E = 102°
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It is 4t because you have to minus it and then you get 4t
Answer:
Step-by-step explanation:
<1 + <2 = 180 degrees (straight angle)
<3 + <5 + <4 = 180 degrees (straight angle)
<1 = <3 (vertical angles)
<1+<2 = <3+<4+<5 (straight angles)
<2 = (<3-<1)+<4+<5 (<3 - <1 = 0)
<2 = <4 + <5
The answer is 110 adult tickets. Let x= student tickets and y= adult tickets.
We know that the total tickets sold was 440. That means the total number of student tickets (x) plus the total number of adult tickets (y) equaled 440. Putting it into an equation, you get:
x+y=440
Now we know that the amount of student tickets is equal to three times as many adult tickets, so in an equation that is seen as:
x=3y
In order to solve for one variable, plug in 3y for the x value of the first equation to get:
y+3y=440
then solve:
4y=440
y= 440/4
y=110
The total number of adult tickets sold was 110 tickets.
(This method used in math is technically called "Solving Systems of Equations", just fyi).
