Question

Among two supplementary angles the measure of the larger angles is 52° more than the measure of the smaller. Find their measures.​

Answer 1

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Among two supplementary angles the measure of the larger angles is 52° more than the measure of the smaller. Find their measures.

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$\huge\boxed{\blue{Given :}}$

➣ Two Supplementary Angles

➣ Larger Supplementary Angle measure 52° more than the measure of the smaller Supplementary Angle

$\huge\boxed{\red{To \: Find :}}$

➣ The Measure of the Smaller Supplementary Angle

➣ The Measure of the Larger Supplementary Angle

$\huge\boxed{\pink {Solution :}}$

➪ Let the Smaller Supplementary Angle = x°

➪ Let the Larger Supplementary Angle = x° + 52°

➪ The Sum of two Supplementary Angles = 180°

⇒ x + 52° + x = 180°

⇒ 2x + 52° = 180°

⇒ 2x = 180° - 52°

⇒ 2x = 128°

⇒ x = $\cancel\frac{128} {2}$

⇒ x = 64°

➣ Smaller Supplementary Angle = x° = 64°

➣ Larger Supplementary Angle = x + 52° = 64° + 52° = 116°

➦ So, the measure of the smaller supplementary angle is 64° and the measure of the larger supplementary angle is 116°

Answer 2

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