Question

( a + 30 drgee) 2a drgee are the measurse of two supplement angle find the value of a and the measurse of each angle​

Answer 1

Given :

• $\sf{ \angle 1 }$ = (a + 30)°
• $\sf{ \angle 2 }$ = 2a°

To Find :

• Value of a
• The angles

$\\ \qquad{\rule{200pt}{2pt}}$

SolutioN :

$\dag$ We know That :

• ${\underline{\boxed{\pmb{\sf{ Sum \; of \; Supplementary \; Angles = {180}^{ \circ } }}}}}$

$\dag$ Calculating the Value of a :

${\longmapsto{\qquad{\sf{ \bigg(a + 30 \bigg)^{ \circ } + {2a}^{ \circ } = {180}^{ \circ } }}}} \\ \\ \\ \\ \ {\longmapsto{\qquad{\sf{ {3a + 30}^{ \circ } = {180}^{ \circ } }}}} \\ \\ \\ \\ \ {\longmapsto{\qquad{\sf{ 3a = 150 }}}} \\ \\ \\ \\ \ {\longmapsto{\qquad{\sf{ a = \dfrac{150}{3} }}}} \\ \\ \\ \\ \ {\longmapsto{\qquad{\sf{ a = \cancel\dfrac{150}{3} }}}} \\ \\ \\ \\ \ {\longmapsto \; {\qquad \; {\pmb{\underline{\boxed{\orange{\frak{ a = 50 }}}}}}}}$

$\dag$ Calculating the Angles :

• $\sf{ \angle 1 = (a + 30)^{ \circ } = (50 + 30)^{ \circ } = 80^{ \circ} }$
• $\sf{ \angle 2 = 2a^{ \circ } = 2 \times 50^{ \circ } = 100^{ \circ} }$

$\therefore \;$ The two angles are 80° and 100° .

$\\ \qquad{\rule{200pt}{2pt}}$

Answer 2

Given:-

/_1=(a+30)°

/_2=2a°

To find :-

• Values of the angles

Solution:-

$\large\underline{\sf{We \: know \: that:}}$

$\large\underline{\sf{Supplementary \:angles = 180 \degree }}$

So,

Sum of both angles should be 180°.

Hence,

The equation formed is

$\large\underline{\sf{ \implies(a + 30 \degree) + 2a = 180 \degree}}$

On solving the equation we get:-

$\large\underline{\sf{ \implies a + 30 \degree + 2a = 180 \degree}}$

$\large\underline{\sf{ \implies3a + 30 \degree = 180 \degree}}$

$\large\underline{\sf{ \implies3a = 180 \degree - 30 \degree}}$

$\large\underline{\sf{ \implies3a = 150 \degree}}$

$\large\underline{\sf{ \implies a = \frac{150 \degree}{3} }}$

$\large\underline{\sf{ \implies a = 50 \degree}}$

On calculating the values we get:-

First angle-»

$\large\underline{\sf{ \implies a + 30 \degree}}$

$\large\underline{\sf{ \implies 50 \degree + 30 \degree }}$

$\large\boxed{\sf{ \boxed{ \red{ \implies 80 \degree}}}}$

Second angle-»

$\large\underline{\sf{ \implies2a}}$

$\large\underline{\sf{ \implies2 \times 50 \degree}}$

$\large\boxed{\sf{ \boxed { \red{\implies100 \degree}}}}$

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Basic concept:-

=>Sum of supplementary angles=180°

=>Sum of complementary angles=90°