Question

The measure of two supplementary angles is (4a + 30)° and (a + 5)°. Find the value of a.​ explain in steps
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Answer 1

Given :

• Measure of two supplementary angles = (4a + 30)° and (a + 5)°

To find :

• the value of a

Solution :

⇒ Let's find the value of a.

• The measure of two supplementary angles = 180°

$\sf \to (4a + 30)^{\circ} + (a + 5)^{\circ} = 180^{\circ}$

$\sf \to (4a + a)^{\circ} + (30 + 5)^{\circ} = 180^{\circ}$

$\sf \to (5a)^{\circ} + (35)^{\circ} = 180^{\circ}$

$\sf \to (5a)^{\circ} = (180^{\circ} - 35)^{\circ}$

$\sf \to 5a^{\circ} = 180^{\circ} - 35^{\circ}$

$\sf \to 5a^{\circ} = 145^{\circ}$

$\sf \to a = \dfrac{145^{\circ}}{5}$

$\sf \to a = \cancel {\dfrac{145^{\circ}}{5}}$

$\sf \to a = 29^{\circ}$

• Therefore, the value of a is 29°.

⇒ Let's find the angles.

$\sf \to (4a + 30)^{\circ}$

$\sf \to (4 \times 29^{\circ} + 30^{\circ})$

$\sf \to (116^{\circ} + 30^{\circ})$

$\sf \to 146^{\circ}$

$\sf \to (a + 5)^{\circ}$

$\sf \to (29 + 5)^{\circ}$

$\sf \to 34^{\circ}$

• Therefore, the angles are 146° and 34°.

Answer 2

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