Question

One of the exterior angle of a triangle is 108°. If one of the opposite interior angle is 72°, then find the other two angles of the triangle. Also state what type of a triangle is this?​

Answer 1

Answer:

72 + x = 108 ( Exterior Angle Property )

x = 108 - 72

x = 36 ( Second Angle)

To find third angle, we can use Angle sum property,

72 + 36 + y = 180

y = 180 - 72 - 36

y = 36 ( Third Angle )

First Angle - 72

Second Angle - 36

Third Angle - 36

Two angles are equal hence it is a Isosceles triangle.

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Answer 2

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Required answer :↴

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• Measures of angles of triangle is 72°, 72° and 36°
• Triangle is Acute triangle.

Explanation :↴

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GivEn:

• Measures of exterior angle of triangle is 108°
• Measures of one opposite interior angle is 72°

To finD:

1. Measures of other two interior angle
2. State type of triangle

Solution:

In this question, we have given that one exterior angle of triangle is 108° and one interior opposite angle is 72°. We have to find it two another interior angle in which one is opposite interior angle.

Knowledge required :

To solve this problem, we need some knowledge about property of triangle. According to the exterior angle property of triangle, measures of exterior angle of triangle is equal to two interior opposite angles of triangle, And according to the angle sum property of triangle, sum of interior angles of triangle is always equal to 180°.

Finding measures on angles :

Here,

We know that measures of exterior angle is 108° and one opposite angle is 72°. Let suppose that another opposite interior angle of triangle is 'x'.

According to the given condition:

• Exterior angle of triangle = sum of two interior opposite angles. { according to the exterior angle property of triangle }

Substituting value in this :

108° = 72° + x ••••( ∵one interior opposite angle is 72° given)

⟹ x = 108° - 72°

⟹ x = 36°

$\large{\sf{\underline{\pink{ ∴ measures ~of~ another~ interior ~opposite~ angles ~is~ 36° }}}}$

Now,

We found that two interior angle of triangle is 72° and 36° respectively.

Now,

Supposing that required interior angle's measures is a.

According to the angle sum property of triangle,

72° + 36° + a = 180°

⟹ 108° + a = 180°

⟹ a = 180° - 108°

⟹ a = 72°

$\large{\sf{\underline{\pink{ ∴Another~ interior~ angle's ~measures~ is ~72°}}}}$

Therefore all angles of traingle is :-

• first angle = 72°
• Second angle is = 72°
• Third angle is = 36°

Finding type of triangle:

In this triangle, we found that measures of all angles of triangle are 72°, 72° and 36° respectively.

Now,

In this triangle, we found that all angles are less than 90° (< 90°).

$\large{\sf{\underline{\pink{ ∴ This \: triangle~ is~ acute~ triangle }}}}$

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Some thing about types of triangle:

Type of triangles are classified as :

• $\large{\sf{\green{\underline{ Based~ on~ length~ of ~their~ sides}}}}$

According to the length of sides, triangles are classified into 3 types.

• Scalene triangle: Triangle are said to be scalene when none side of triangle is equal to another side of same triangle.
• Isosceles triangle: Triangle are said to be isosceles when length of two side of same triangle is equal
• Equilateral triangle: Triangle are said to be equilateral when all sides of triangle are of equal measures.

• $\large{\sf{\green{\underline{ Based ~on~ measures ~of ~angles}}}}$

According to the measures of angles of triangle, triangle is classified into 3 types :

• Acute triangle: Triangle are said to be acute angled triangle when all sides of triangle is less than 90°
• Obtuse triangle: Triangle are said to be obtuse when the one angle of triangle is greater then 90°
• Right triangle : Triangle are said to be right angled triangle when one angle of triangle is equal to 90°