Question

A right triangle has one angle that measures 15º. What is the measure of the other acute

angle?

Answer 1

`\bigstar \underline\frak{Required \: Solution}`

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Given :-

• Triangle is a right triangle
• One angle of triangle = 15°

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To find :-

• Left angle of triangle.

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So first you should know what is right triangle ?

A triangle which has one angle as 90° and other two angles are acute angle.

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So we get know that one angle of triangle is 90°

Now :-

`\star \boxed{\angle 1 + \angle 2 + \angle 3 = 180\degree}`

Reason :-

Sum of angles of triangle is equal to 180°

Formula :-

• sum = (no. of angles - 2) × 180°
• Sum = (3 - 2) × 180°
• Sum = 1 × 180°
• Sum = 189°

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Steps to find left angle :-

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`\sf\dashrightarrow\angle 1 + \angle 2 + \angle 3 = 180\degree`

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`\sf\dashrightarrow90 + 15 + \angle 3 = 180\degree`

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`\sf\dashrightarrow105 + \angle 3 = 180\degree`

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`\sf\dashrightarrow\angle 3 = 180\degree - 105 \degree`

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`\bf\dashrightarrow\angle 3 = 75\degree`

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.°. measurement of left angle is 75°

Answer 2

75°

Explanation:

• The sum of interior angles of a triangle is 180°
• Right angle = 90°
• Acute angle is an angle that measures less than 90°

Let x = unknown angle

Therefore, if a right triangle has one angle that measures 15°:

⇒ x + 15 + 90 = 180

⇒ x + 105 = 180

⇒ x = 180 - 105

⇒ x = 75°