Question

5. Two angles are supplementary. The larger angle 120

greater than the twice the measure of

the smaller angle. Find the measure of each ​

Answer 1

Solution :

$\bf{\red{\underline{\bf{Given\::}}}}$

Two angles are supplementary. The larger angle 120 greater than twice the measure of the smaller angle.

$\bf{\red{\underline{\bf{To\:find\::}}}}$

The measure of each angle.

$\bf{\red{\underline{\bf{Explanation\::}}}}$

Let the smaller angle be r°

Let the larger angle be (2r + 120)°

We know that sum of two angles equal to 180° is know as supplementary.

A/q

$\longrightarrow\sf{r+2r+120\degree=180\degree}\\\\\\\longrightarrow\sf{3r+120\degree=180\degree}\\\\\\\longrightarrow\sf{3r=180\degree-120\degree}\\\\\\\longrightarrow\sf{3r=60\degree}\\\\\\\longrightarrow\sf{r=\cancel{\dfrac{60\degree}{3} }}\\\\\\\longrightarrow\sf{\pink{r=20\degree}}$

Thus;

$\underbrace{\sf{The\:smaller\:angle=r=\boxed{20\degree}}}}}\\\underbrace{\sf{The\:larger\:angle=(2r+120\degree)=(2\times 20+120)=(40+120)\degree=\boxed{160\degree}}}}}$

Answer 2

Aɴꜱᴡᴇʀ

☞ Smaller angle = 20°

☞ Larger angle = 160°

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Gɪᴠᴇɴ

✒ Two angles are supplementary

✒ The larger angle is 120° greater than twice the measure of the smaller angle

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Tᴏ ꜰɪɴᴅ

◕ The measure of each angle?

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Sᴛᴇᴘꜱ

❍ First to find you answer we have to do some assumption,that is

➠ Let smaller angle be x° , So then the larger angle will be (2x + 120)°

If you see the Question its given that it is a supplementary angle, that is their sum is 180°

➳ x + 2x + 120° = 180°

➳ 3x = 180° - 120°

➳ 3x = 60°

➳ x = $\sf\dfrac{60}{3}$

➳ $\sf{\pink{20°}}$

So now lets calculate the larger angle

➤ 2x + 120°

➤ 2(20) + 120°

➤ 40° + 120°

➤$\sf{\pink{160°}}$

Verification

We know that the sum of the larger and the smaller angle is 180°, so

✭ 20° + 160° = 180°

Thus verified.

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