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Standard VII

Mathematics

Exterior Angle Property

In Δ DEF, an ...

Question

In $Δ$ DEF, an exterior angle at F is (8x + 15). If the two non-adjacent interior angles are (4x + 5) and (3x + 20), find the value of that exterior angle (in degrees).

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Solution

The correct option is D
95

A measure of an exterior angle of a triangle is equal to the sum of the measures of the interior opposite angles.

8x + 15= (4x + 5) + (3x + 20)
8x + 15 = 7x + 25
8x – 7x = 25 – 15
x = 10

So, exterior angle = 8x + 15 = 8 × 10 + 15 = 95 $^{\circ}$

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In ΔDEF, an exterior angle at F is (8x + 15). If the two non-adjacent interior angles are (4x + 5) and (3x + 20), find the value of that exterior angle (in degrees).

The correct option is D 95 A measure of an exterior angle of a triangle is equal to the sum of the measures of the interior opposite angles. 8x + 15= (4x + 5) + (3x + 20) 8x + 15 = 7x + 25 8x – 7x = 25 – 15 x = 10 So, exterior angle = 8x + 15 = 8 × 10 + 15 = 95∘

In $Δ$ DEF, an exterior angle at F is (8x + 15). If the two non-adjacent interior angles are (4x + 5) and (3x + 20), find the value of that exterior angle (in degrees).

The correct option is D
95

A measure of an exterior angle of a triangle is equal to the sum of the measures of the interior opposite angles.

8x + 15= (4x + 5) + (3x + 20)
8x + 15 = 7x + 25
8x – 7x = 25 – 15
x = 10

So, exterior angle = 8x + 15 = 8 × 10 + 15 = 95 $^{\circ}$