Question

Among two supplementary angles, the measure of the longer angle is 44 more
than the measure of the smaller angle. Find their measures.​

Answer 1

Among two supplementary angles, the measure of the longer angle is 44 more than the measure of the smaller angle.

Let us consider that

• Measure of the smaller angle = k
• Measure of the larger angle = k + 44

As we know that, sum of two supplementary angles is 180°.

Now, according to question -

• ➝ k + (k + 44) = 180°
• ➝ k + k + 44 = 180°
• ➝ 2k + 44 = 180°
• ➝ 2k = 180° - 44
• ➝ 2k = 136
• ➝ k = 136/2
• ➝ k = 68

Put the value of k

• First angle → k → 68°
• Second angle → k + 44 = 68 + 44 → 112°

Verification -

• ➝ k + k + 44 = 180°
• ➝ 68 + 68 + 44 = 180°
• ➝ 68 + 112 = 180°
• ➝ 180° = 180°

Hence, verified !

Answer 2

Answer:

WHAT ARE SUPPLEMENTARY ANGLES:

Two angles whose measure is equal to

$180 \degree \: is \: called \: supplementry \:angle$

Now according to the above definition

$\bf \red{let \: the \: angles \: be} \\ \bf \green{x \: and \: y} \\ \tt(x \:is \: longer) \\ \bf\purple{according \: to \: the \: question} \\ \bf\purple{longer \: angle(x)is} \\ \bf\purple{44 \: larger \: than \: y} \\ \bf\purple{so \:value \: of \: x = y + 44} \\ \bf\blue{y + (y + 44) = 180 \degree} \\ \bf\blue{2y + 44 = 180 \degree} \\ \bf\blue{2y = 180 - 44 = 126} \\ \bf\blue{2y = 126} \\ \bf\blue{y = \cancel \frac{126}{2} = 63 } \\ \bf\purple{so \: } \\ \bf\purple{value \: of \: y = 63 \degree} \\\bf\purple{we \: know \: that} \\ \bf\green{x = y + 44} \\ \bf\purple{so} \\ \bf\green{x = 63 + 44 = 107} \\ \bf {verification \:\pink\to\: 63 + 107 = 180 \degree}$

Related Angle

1. Complementary Angle: Two angles whose measure is equal to $90 \degree \: is \: called \: supplementry \:angle$