4(x-2)-3=9
<span>Reorder the terms:
4(-2 + x) + -3 = 9
</span><span>(-2 * 4 + x * 4) + -3 = 9
</span><span>(-8 + 4x) + -3 = 9
</span><span>Reorder the terms:
-8 + -3 + 4x = 9
</span><span>Combine like terms:
-8 + -3 = -11
</span>-11 + 4x = 9
<span>Solving:
-11 + 4x = 9
</span>Add '11' to each side of the equation.
-11 + 11 + 4x = 9 + 11
Combine like terms: -11 + 11 = 0
0 + 4x = 9 + 11
4x = 9 + 11
<span>Combine like terms:
9 + 11 = 20
4x = 20
</span><span>Divide each side by 4.
x = 5</span>
Answers:
x = 5
m∠C = m∠H = 38 degrees
WORKINGS
Given that ABCD ≅ FGHJ
We know that corresponding angles of two congruent
quadrilaterals are equal
Therefore,
m∠A = m∠F
m∠B = m∠G
m∠C = m∠H
m∠D = m∠I
Given,
m∠C = 9x – 7
m∠H = 5x + 13
Since m∠C = m∠H
9x – 7 = 5x + 13
Add 7 to both sides of the equation
9x – 7 + 7 = 5x + 13 + 7
9x = 5x + 20
Subtract 5x from both sides of the equation
9x – 5x = 5x – 5x + 20
4x = 20
Divide both sides of the equation by 4
4x/4 = 20/4
x = 5
To determine the measures of angle C and angle H
m∠C = m∠H
We know that m∠C = 9x – 7
Since x = 5
m∠C = 9(5) – 7
m∠C = 45 – 7
m∠C = 38
Therefore, m∠C = m∠H = 38 degrees
Yes, it is also a square number
3180 because you divide 31800 by 10
