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,
[tex](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[/tex]
[tex]\boxed{\pink{\sf\leadsto Value \ of \ x \ is \ 24^{\circ}}}[/tex]
[tex]\boxed{\pink{\sf\leadsto Value \ of \ \angle C \ is \ 60^{\circ}}}[/tex]
[tex]\boxed{\pink{\sf\leadsto Value \ of \ \angle D \ is \ 120^{\circ}}}[/tex]
A parallelogram is given to us . in which m ∠ B = 5x and m ∠C = 2x + 12 ° . And we need to find x .
Figure :-
[tex]\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}[/tex]
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° .
[tex]\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}}}}[/tex]
[tex]\rule{200}2[/tex]
Q. no. 2 ) Determine the measure of < C .
Here we can see that <C = 2x + 12 ° . So ,
[tex]\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}}}}[/tex]
[tex]\rule{200}2[/tex]
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° .
[tex]\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}}}}[/tex]