Question

12.
The measures of angles of a triangle are in the
ratio 2: 6:7. Find their measures in degrees.​

Answer 1

Cᴏʀʀᴇᴄᴛ Qᴜᴇsᴛɪᴏɴ :-

The measures of angles of a triangle are in the

ratio 2: 6:7. Find their measures in degrees.

Gɪᴠᴇɴ :-

Ratio between the angles of a triangle = 2:6:7.

Tᴏ Fɪɴᴅ :-

Find their measures in degrees.

Sᴏʟᴜᴛɪᴏɴ :-

Let the angles be 2x,6x and 7x respectively.

We know that,

Sum of all three intererior angles of a triangle = 180°.

So we write,

$\sf\large\purple{⇝2x + 6x + 7x = 180°}$

$\sf\large\purple{⇝15x = 180°}$

$\sf\large\purple{⇝x = \frac{180}{15} }$

$\sf\large\purple{⇝x = 12°}$

Hence all the three interior angles of a triangle are :-

$\sf\large\blue{⇝2x = 2 \times 12 = 24° }$

$\sf\large\blue{⇝6x = 6 \times 12 = 72° }$

$\sf\large\blue{⇝7x = 7 \times 12 = 84°}$

Vᴇʀɪғɪᴄᴀᴛɪᴏɴ :-

$\sf\large\pink{24° + 72° + 84° = 180°}$

$\large\green{\mathtt{Hence\:Verifed!!}}$