If (2x−10°) and (3x−50°) are complementary angles, then the value of (4x+ 40°) is :

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160°

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160°

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The correct option is 160°.

Step 1: Understand the definition of complementary angles

Two angles are said to be complementary if the sum of their measures is equal to 90°.

Step 2: Set up the equation

Given the two complementary angles are (2x − 10°) and (3x − 50°), we can write:

$(2x-10°)+(3x-50°)=90°$

Step 3: Solve for x

Combine the like terms on the left side of the equation:

$2x+3x-10°-50°=90°$

$5x-60°=90°$

Add 60° to both sides of the equation:

$5x=90°+60°$

$5x=150°$

Divide both sides by 5:

$x=\frac{150°}{5}$

$x=30°$

Step 4: Find the value of (4x + 40°)

Substitute x = 30° into the expression (4x + 40°):

$4x+40°=4(30°)+40°$

$4x+40°=120°+40°$

$4x+40°=160°$

Thus, the value of (4x + 40°) is 160°.

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`. Checked. 4. Clean tags `` and ``. Checked. 160°

The correct option is 160°.

Step 1: Understand the definition of complementary angles

Two angles are complementary if the sum of their measures equals 90°.

Step 2: Set up the algebraic equation

Given that (2x − 10°) and (3x − 50°) are complementary angles, their sum must be 90°:

$(2x-10°)+(3x-50°)=90°$

Step 3: Solve for x

Combine the like terms on the left side of the equation:

$2x+3x-10°-50°=90°$

$5x-60°=90°$

Add 60° to both sides:

$5x=90°+60°$

$5x=150°$

Divide both sides by 5:

$x=\frac{150°}{5}$

$x=30°$

Step 4: Calculate the required value of (4x + 40°)

Substitute x = 30° into the given expression:

$4x+40°=4(30°)+40°$

$4x+40°=120°+40°$

$4x+40°=160°$

Therefore, the value of (4x + 40°) is 160°.