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3 years ago

AB = x + 8

Mathematics

1 answer:

vivado [14]3 years ago

3 0

Answer: The length of BC is 7

Step-by-step explanation: Assuming the lengths of the opposite sides of the quadrilateral are congruent, then

AB=DC and

AD=BC

Inputting the values of AB, DC and AD as given in the question:

x + 8 = 3x ...(1)

x + 3=? ...(2)

We have to solve for the value of x to get the actual lengths and thus ascertain BD.

From equation (1):

8 = 3x - x

8 = 2x

8/2 = x

Therefore, x = 4.

If x = 4 then equation(2) would be

4 + 3= 7.

Hence, the actual lengths of the quadrilateral are:

AB = 4 + 8. DC = 3(4)

=12. =12.

AD = 4 + 3. AD = BC

= 7. Therefore, BC = 7.

Hence, it is confirmed that quadrilateral ABCD is a parallelogram since both the opposite sides are proven to be congruent.

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<h2>○=> <u>Correct option</u> :</h2><h2> $\color{hotpink}\bold{ (a) \: 130}$ </h2><h3>○=> <u>Steps to derive correct option</u> :</h3>

Angle (p+7)° and angle (3p+1)° are a linear pair so their sum will be equal to 180°.

Which means :

$=\tt 3p + 1 + p + 7 = 180$

Let us solve that equation to find the value of p and the two angles :

$=\tt 3p + 1 + p + 7 = 180$

$=\tt 3p + p + 1 + 7 = 180$

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$= \tt4p = 180 - 8$

$= \tt4p = 172$

$=\tt p = \frac{172}{4}$

$\hookrightarrow \tt \color{plum}p = 43$

Thus, value of p = 43

Measure of angle (p+7)° :

$=\tt 43 + 7$

$\tt\color{plum}angle \: (p + 7)° =\tt 50°$

Measure of angle (3p+1)° :

$=\tt 43 \times 3 + 1$

$= \tt129 + 1$

$\tt\color{plum}angle \: (3p + 1)° = 130°$

Thus, the measure of the larger angle = 130°

Therefore, the correct option is <em>(a) 130</em>

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