Question

One of the exterior angles of a triangle is 105°and the interior opposite angles are in the ratio 2:5 .Find the angles of the triangle.

Answer 1

2x+5x=105
7x=105
x=15
one angle=30
other angle=75

Answer 2

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✬ Angles = 30° ,75° & 75° ✬

Step-by-step explanation:

Given:

Measure of exterior angle of triangle is 105°.

Ratio of opposite angles of triangle is 2 : 5.

To Find:

Measure of angles of triangle ?

Solution: Let x be the common in given ratios and ABC be a triangle.

Here in triangle ABC we have

∠ACD = exterior angle of ∆.

∠BAC : ∠CBA = 2 : 5.

[ Remind a theorem ]

The sum of exterior angle of a triangle is equal to the sum of its opposite interior angles.

∠BAC & ∠CBA are opposite interior angles.

⟹ ∠BAC + ∠CBA = ∠ACD

⟹ 2x + 5x = 105°

⟹ 7x = 105°

⟹ x = 105°/7

⟹ x = 15°

So , measure of

∠BAC = 2 × 15 = 30°

∠CBA = 5 × 15 = 75°

Now by using a property of triangle.

[ Angle sum property ]

It states that sum of all interior angles of a ∆ is equal to 180°.

➟ ∠BAC + ∠CBA + ∠ACB = 180°

➟ 30° + 75° + ∠ACB = 180°

➟ ∠ACB = 180° – 105°

➟ ∠ACB = 75°