Question

please help me
answer this question please
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Answer 1

Answer:

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

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

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

Step-by-step explanation:

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

Figure :-

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

Q. no. 1 ) Find the value of x.

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° .

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

Hence the value of x is 24° .

$\rule{200}2$

Q. no. 2 ) Determine the measure of < C .

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

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

Hence the value of <C is 60°.

$\rule{200}2$

Q. no. 3 ) Determine the measure of < D .How you determined the answer .

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° .

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

Hence the value of <D is 120° .