Question

the measure of an angel is 8 times its complement find the angel​

Answer 1

Answer:

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Answer 2

$\pink\bigstar$ Correct Question:

• The measure of an angle is 8 times of its complement. Find the angle.

$\blue\bigstar$Answer:

$\boxed{x\: = \:{80}^{\circ}\:}$

$\green\bigstar$ Given:

• The measure of an angle is 8 times of its complement.

$\red\bigstar$To find:

• The unknown angle.

$\pink\bigstar$ Solution:

Let the unknown angle be x.

$\hookrightarrow$ $\therefore$the angle is x.

It's complementary angle:

$\hookrightarrow$ ( 90° - x )

( $\because$ sum of complementary angles is 90° )

The unknown angle is 8 times of its complement:

$\hookrightarrow$ x = 8 (90° - x )

Now, by equating the expressions and solving them:

x = 8 ( 90° - x )

$\implies$ x = 720° - 8x

$\implies$ x + 8x = 720°

( By transposition method)

$\implies$ 9x = 720°

$\implies$ x = $\dfrac{{720}^{\circ}}{9}$

$\implies$ $\boxed{x\: = \:{80}^{\circ}\:}$

$\boxed{\therefore x\: = \:{80}^{\circ}\:}$

$\blue\bigstar$ Concepts Used:

• Assumption of unknown angle.
• Sum of complementary angles is 90°.
• Making expressions from variable
• Equation of given expressions
• Transposition Method

$\green\bigstar$Extra - Information:

• Sum of Supplementary angles is 180°
• The angles are said to be linear if they are adjacent to each other after the intersection of the two lines. The sum of angles of a linear pair is always equal to 180°.
• Acute angle - An angle between 0° and 90°.
• Right angle - An 90° angle
• Obtuse angle - An angle between 90° and 180°
• Straight angle - A 180° angle
• Reflex angle - An angle between 180° and 270°
• Complete angle - A 360° angle