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aleksley [76]
3 years ago
7

Given the lines a and b are parallel and that m<8=180, find

Mathematics
1 answer:
anygoal [31]3 years ago
7 0

Answer:

  • D) 72°

Step-by-step explanation:

Sum of angles 7 and 8 is 180° as they are supplementary

Angles 7 and 3 are corresponding angles and they measure same as per property of corresponding angles, therefore:

  • m∠3 = m∠7
  • m∠7 = 180° - m∠8 = 180° - 108° = 72°
  • So m∠3 = 72°

Option D is correct

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The diagonals of a rhombus measures 6cm and 8cm, what is the perimeter of this rhombus?
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<h2><u>Diagram</u><u>:</u><u>-</u></h2>

\setlength{\unitlength}{1 cm}\begin{picture}(20,15)\thicklines\qbezier(1,1)(1,1)(6,1)\qbezier(1,1)(1,1)(1.6,4)\qbezier(1.6,4)(1.6,4)(6.6,4)\qbezier(6,1)(6,1)(6.6,4)\qbezier(6.6,4)(6.6,4)(1,1)\qbezier(1.6,4)(1.6,4)(6,1)\put(0.7,0.5){\sf A}\put(6,0.5){\sf B}\put(1.4,4.3){\sf D}\put(6.6,4.3){\sf C}\end{picture}

<h3><u>Required Answer</u><u>:</u><u>-</u></h3>

The diagonals of the Rhombus= d1 & d2=6cm and 8cm

Let the Side=a

As we know that in a Rhombus

{\boxed{\sf side=\sqrt {\left ({\dfrac{d1}{2}}\right)^2+\left ({\dfrac {d2}{2}}\right)^2}}}

  • Substitute the values

{:}\longmapsto\sf a=\sqrt {\left ({\dfrac {6}{2}}\right)^2+\left ({\dfrac {8}{2}}\right)^2 }

{:}\longmapsto\sf a=\sqrt {(3)^2+(4)^2}

{:}\longmapsto\sf a=\sqrt {9+16}

{:}\longmapsto\sf a=\sqrt{25}

{:}\longmapsto\sf a=5cm

<h2>_____________</h2><h3>Again </h3>

we know that in a Rhombus

\boxed{\sf Perimeter=4a}

  • Substitute the values

{:}\longmapsto\sf Perimeter=4×5

{:}\longmapsto\sf Perimeter=20cm

\thereforePerimeter of the rectangle is 20cm.

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Complementary angles sum to 90°.

<u>∠X has </u><u>∠P </u><u>complementary to it as:</u>

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