Question

Two supplementary angles differ by 20°. Find the measure of the smaller
angle.

Answer 1

Given:-

• Two supplementary angles different by 20°.

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To find:-

• The measure of the smaller angle.

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Solution:-

Let,

• the larger angle be x°.

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Then,

• the smaller angle will be x - 20°.

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Note:- Two angles are supplementary if their sum is 180°.

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→ x + (x - 20) = 180

→ 2x = 180 + 20

→ 2x = 200

→ x = 200/2

→ x = 100°

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Hence,

• the smaller angle is 100° - 20° = 80°

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Diagram:-

$\setlength{\unitlength}{1 cm}\begin{picture}(0,0)\thicklines\put(5,1){\vector(1,0){4}}\put(5,1){\vector(-1,0){4}}\put(5,1){\vector(1,1){3}}\put(2,2){ \underline{\boxed{\large\sf 100 + 80 = 180^{\circ}} }}\put(4.5,1.3){ \sf x^{\circ} }\put(5.7,1.3){ \sf (x - 20)^{\circ} }\end{picture}$

Answer 2

Solution :

Given that, two supplementary angles differ by 20°.

We've to find the measurement of smaller angle.

Steps :

As we know that here are two supplementary angles and we've read earlier that sum of two supplementary angles is 180° ; let us assume that larger angle is k and smaller angle is (k - 20) as they differ by 20.

Angles are :

• k
• (k - 20)

Now, according to question :

➥ k + (k - 20) = 180

➥ k + k - 20 = 180

➥ 2k - 20 = 180

➥ 2k = 180 + 20

➥ 2k = 200

➥ k = 200/2

➥ k = 100°

Now

• Larger angle = k => 100°
• Smaller angle = k - 20 = 100 - 20 => 80°