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2 years ago

Segment RS and segment ST below are congruent. Set up ban equation to find the value of x

Mathematics

1 answer:

borishaifa [10]2 years ago

3 0

Answer:

x = 11

Step-by-step explanation:

If the segments are congruent then

3x = x + 22 ➡ 3x - x = 22

2x = 22 divide both sides by 2

x = 11

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Liula [17]

SOLUTION

Consider the property, opposite angle of a cyclic quadrilateral are supplementary

hence

$\angle NMP+\angle NOP=180^0$

Recall that

$\begin{gathered} \angle NMP=\angle M=(8x-24)^0 \\ \text{and } \\ \angle NOP=\angle O=(4x)^0 \end{gathered}$

Hnece, we have that

$\begin{gathered} \angle M+\angle O=180^0(opposite\text{ angles of a cyclic quadrilateral)} \\ (8x-24)^0+4x^0=180^0 \end{gathered}$

Then

$\begin{gathered} 8x-24+4x=180 \\ 8x+4x-24=180 \\ 12x-24=180 \\ \text{Add 24 t o both sides } \\ 12x-24+24=180+24 \\ 12x=204 \\ \text{divide both sides by 12} \\ \frac{12x}{12}=\frac{204}{12} \\ \text{Then} \\ x=17 \end{gathered}$

Hence

x=17

Since

$\begin{gathered} \angle NOP=(4x)^0 \\ \text{substitute the value of x, we have } \\ \angle NOP=4\times17=68^0 \\ \text{Hence } \\ \angle NOP=68^0 \end{gathered}$

Therefore

The measure of angle NOP is 68⁰

Answer; 68⁰ (The fourth Option )

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1 year ago

6(2x+4)=4(3x+6) solve and show work

Afina-wow [57]

Answer:

0=0

Step-by-step explanation:

6(2x+4)=4(3x+6)

Step 1: Simplify both sides of the equation.

6(2x+4)=4(3x+6)

(6)(2x)+(6)(4)=(4)(3x)+(4)(6)(Distribute)

12x+24=12x+24

Step 2: Subtract 12x from both sides.

12x+24−12x=12x+24−12x

24=24

Step 3: Subtract 24 from both sides.

24−24=24−24

0=0

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