Quadrilateral EFGH is a rectangle. If EM equals 5X plus one and HF equals 42 find the value of X
Quadrilateral ABCD is a rectangle. Find the value of "x" if m/_DAC=(4x+8)degrees and m/_ CAB=(5x-8) degrees
if m is at the center then diagonal = 2(5x+1)
which is the same as the other diagonal 42
5x+1 = 21
5x = 20
x = 4
The angles are both in corner A
so they add up to 90 degrees
4x+8 = 5x-8
x = 16
how to find angles
To find the value of X in the first question, we need to set up an equation using the properties of a rectangle.
In a rectangle, opposite sides are equal in length. Since EFGH is a rectangle, we know that the length of segment EM is equal to the length of segment HF.
Given that EM = 5X + 1 and HF = 42, we can set up the equation:
5X + 1 = 42
Now we can solve for X by isolating the variable:
5X = 42 - 1
5X = 41
X = 41/5
X = 8.2
Therefore, the value of X is 8.2.
In the second question, we need to use the properties of a rectangle to find the value of x.
Since ABCD is a rectangle, opposite angles are equal. We are given two angles: m/∠DAC = (4x + 8) degrees and m/∠CAB = (5x - 8) degrees.
To find the value of x, we can set up an equation by equating the two angles:
4x + 8 = 5x - 8
Now we can solve for x by isolating the variable:
8 + 8 = 5x - 4x
16 = x
Therefore, the value of x is 16.