Question

Measures of three angles of a triangle are 2x ,(3x + 15) and (8x-30), the measures of angles are

30 , 60 , 90,

45 , 45 , 90

60 , 60, 60

none of these


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Answer 1

• The angles of a triangle are 30°, 60°, and 90°

Given:

The angles of a triangle are

• 2x°
• (3x + 15)°
• (8x - 30)°

To find:

The value of the three angles of the triangle

Here is something about a triangle-

• The sum of all three interior angles of a triangle is 180°. [Angle sum property of a triangle]
• A triangle that has three equal sides is called an 'equilateral triangle'. Each angle of an equilateral triangle is 60°.
• If a triangle is having two equal sides (two equal angles) then, it's an isosceles triangle.
• In a scalene triangle, all three sides of a triangle are not the same.

Now,

⇒ 2x + (3x + 15) + (8x - 30) = 180

⇒ 2x + 3x + 15 + 8x - 30 = 180

⇒ 13x - 15 = 180

⇒ 13x = 180 + 15

[By transporting 15 to RHS]

⇒ 13x = 195

⇒ x = 195 ÷ 13

[By transporting 13 to RHS]

⇒ x = 15

• Thus, the value of x is 15

Now,

The angles of the triangle are-

• 2x = 2 * 15 = 30°
• (3x + 15) = (3 * 15 + 15) = 45 + 15 = 60°
• (8x - 30) = (8 * 15 - 30) = (120 - 30) = 90°

Hence,

Option 1. is the correct answer (30, 60, 90)

Answer 2

GIVEN :-

• Measures of three angles of a triangle are 2x , (3x + 15) and (8x - 30) .

TO FIND :-

• The measurement of three angles of the triangle .

SOLUTION :-

We have know that,

✯ ᴛʜᴇ ᴍᴇᴀsᴜʀᴇᴍᴇɴᴛ ᴏғ ᴛʜʀᴇᴇ ᴀɴɢʟᴇs ᴏғ ᴀ ᴛʀɪᴀɴɢʟᴇ ɪs " 180° " .

$\bf{\implies\:2x\:+\:(3x\:+\:15)\:+\:(8x\:-\:30)\:=\:180^{\degree}\:}$

$\rm{\implies\:13x\:-\:15\:=\:180\:}$

$\rm{\implies\:13x\:=\:180\:+\:15\:}$

$\rm{\implies\:x\:=\:\dfrac{195}{13}\:}$

$\bf\green{\implies\:x\:=\:15^{\degree}\:}$

✍️ Hence,

☃️ 2x = 2 × 15 = 30°

☃️ 3x + 15 = 3 × 15 + 15 = 45 + 15 = 60°

☃️ 8x - 30 = 8 × 15 - 30 = 120 - 30 = 90°

$\rule{200}2$

$\orange\star\:\bf{\gray{\underline{\pink{\boxed{\blue{Correct\:Option\:\longrightarrow\:a)\:30^{\degree}\:,\:60^{\degree}\:and\:90^{\degree}\:}}}}}}$