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Verdich [7]
2 years ago
13

Can you do this please​

Mathematics
2 answers:
dezoksy [38]2 years ago
5 0

Answer:

x = 24

Step-by-step explanation:

ABCD is a parallelogram.

Angle B and Angle C are adjacent (successive) angles.

Adjacent angles of a parallelogram are supplementary.

Therefore,

(5x) \degree + (2x + 12) \degree = 180 \degree \\  \\ (5x + 2x + 12) \degree = 180 \degree \\  \\ (7x+ 12) \degree = 180 \degree \\  \\7x+ 12 = 180 \\  \\7x = 180 - 12 \\  \\ 7x = 168 \\  \\ x =  \frac{168}{7}  \\  \\ x = 24

Savatey [412]2 years ago
5 0
<h3><u>Answer:</u></h3>

\boxed{\pink{\sf\leadsto Value \ of \ x \ is \ 24^{\circ}}}

\boxed{\pink{\sf\leadsto Value \ of \ \angle C \ is \ 60^{\circ}}}

\boxed{\pink{\sf\leadsto Value \ of \ \angle D \ is \ 120^{\circ}}}

<h3><u>Step-by-step explanation:</u></h3>

A parallelogram is given to us . in which m ∠ B = 5x and m ∠C = 2x + 12 ° . And we need to find x .

<u>Figure</u><u> </u><u>:</u><u>-</u><u> </u>

\setlength{\unitlength}{1 cm}\begin{picture}(12,12)\thicklines\put(0,0){\line(1,0){5}} \put(5,0){\line(1,2){2}}\put(7,4){\line( - 1,0){5}}\put(2,4){\line( - 1, - 2){2}}\put(0,-0.4){$\bf A$}\put(5,-0.4){$\bf b$}\put(6.5,4.3){$\bf c$}\put(2,4.3){$\bf d$}\qbezier(4.4,0)( 4.5, 0.8)(5.22,0.54)\put(4,0.4){$\bf 5x$}\put(4.7,3.3){$\bf 2x + 12$}\end{picture}

<u>Q. no. 1 ) <em>Find</em><em> </em><em>the</em><em> </em><em>value</em><em> </em><em>of</em><em> </em><em>x</em><em>. </em></u>

Here we can clearly see that ∠DCB and ∠ABC are co - interior angles . And we know that the sum of co interior angles is 180° .

\tt:\implies \angle DCB + \angle ABC = 180^{\circ} \\\\\tt:\implies (2x + 12)^{\circ} + 5x^{\circ}=180^{\circ} \\\\\tt:\implies 7x = (180 - 12 )^{\circ} \\\\\tt:\implies 7x = 168^{\circ} \\\\\tt:\implies x =\dfrac{168^{\circ}}{7} \\\\\underline{\boxed{\red{\tt\longmapsto x = 24^{\circ}}}}

<h3><u>Hence</u><u> </u><u>the</u><u> value</u><u> of</u><u> x</u><u> is</u><u> </u><u>2</u><u>4</u><u>°</u><u> </u><u>.</u></h3>

\rule{200}2

<u>Q</u><u>.</u><u> </u><u>no</u><u>.</u><u> </u><u>2</u><u> </u><u>)</u><u> </u><u>Deter</u><u>mine</u><u> the</u><u> </u><u>meas</u><u>ure</u><u> </u><u>of</u><u> </u><u><</u><u> </u><u>C</u><u> </u><u>.</u>

Here we can see that <C = 2x + 12 ° . So ,

\tt:\implies \angle C =  2x + 12^{\circ}  \\\\\tt:\implies \angle C = 2\times 24^{\circ} + 12^{\circ}  \\\\\tt:\implies \angle C = 48^{\circ} + 12^{\circ}  \\\\\underline{\boxed{\red{\tt\longmapsto \angle C  = 60^{\circ}}}}

<h3><u>Hence</u><u> </u><u>the</u><u> value</u><u> of</u><u> </u><u><</u><u>C</u><u> </u><u>is</u><u> </u><u>6</u><u>0</u><u>°</u><u> </u><u>.</u></h3>

\rule{200}2

<u>Q</u><u>.</u><u> </u><u>no</u><u>.</u><u> </u><u>3</u><u> </u><u>)</u><u> </u><u>Deter</u><u>mine</u><u> the</u><u> measure</u><u> of</u><u> </u><u><</u><u> </u><u>D</u><u> </u><u>.</u><u>How</u><u> </u><u>you</u><u> </u><u>determi</u><u>ned</u><u> </u><u>the</u><u> </u><u>answer</u><u> </u><u>.</u>

Here we can clearly see that ∠D and ∠C are co - interior angles . And we know that the sum of co interior angles is 180° .

\tt:\implies \angle C + \angle D = 180^{\circ} \\\\\tt:\implies 60^{\circ} + \angle D = 180^{\circ}\\\\\tt:\implies  \angle D =  180^{\circ} - 60^{\circ}  \\\\\underline{\boxed{\red{\tt\longmapsto \angle D  = 120^{\circ}}}}

<h3><u>Hence</u><u> </u><u>the</u><u> value</u><u> of</u><u> </u><u><</u><u>D</u><u> </u><u>is</u><u> </u><u>1</u><u>2</u><u>0</u><u>°</u><u> </u><u>.</u></h3>
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