Question

If 2x + 70° and 3x + 20° are supplementary angles determine the value of x?

Answer 1

Answer:

Step-by-step explanation:

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Answer 2

$\Huge{\red{\underline{\textsf{Solution}}}}$

Given -

Two angles which are supplementary

Angle 1 = 2x + 70°

Angle 2 = 3x + 20°

To find -

The value of x

Solution -

♦ The sum of supplementary angles are 180°.

Now , Angle 1 + Angle 2 = 180°

→ (2x + 70°) + (3x + 20°) = 180°

→ 5x + 90° = 180°

→ 5x = 180° - 90°

→ 5x = 90°

→ x = $\sf \dfrac{90°}{5}$

→ x = 18°

$\large\bold{\red{\textsf{\underline{Value\:of\:x\:is\:18°}}}}$

$\rule{200}2$

• Furthermore , substituting value of x so as to get the values of Angle 1 and Angle 2.

Angle 1 = 2x + 70° = 2 (18°) + 70° = 36° + 70° = 106°

Angle 2 = 3x + 20° = 3 (18°) + 20° = 54° + 20° = 74°

$\large\bold{\green{\underline{Verification-}}}$

♦ Angle 1 + Angle 2 = 180°

♦ 106° + 74° = 180°

♦ 180° = 180°

→ Since LHS = RHS , hence proved .

$\rule{200}2$