an exterior angle of a triangle measures 120 degree and its interior opposite angles are in the ratio 5:7. find the angles of the triangles.
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Answer:
Step-by-step explanation:
An exterior angle of a triangle is 120 degrees and one of the interior opposite angles is 30 degrees. What are the other angles of triangles?
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Carter McClung
Carter McClung, High School Geometry Teacher
Answered Dec 20, 2017 · Author has 1.4k answers and 2.6m answer views
Step one, draw a picture!
There are three relevant theorems to help us here:
The angle sum theorem: a + b + c = 180° (interior angles of a triangle sum to 180°)
The linear pair theorem: b + d = 180° (linear pairs are supplementary)
And by combining the two, and a little Algebra, you get
Exterior angle theorem: a + c = d (The exterior angle is equal to the sum of the two remote interior angles)
In the problem, you were given an exterior angle, d = 120°, and a remote interior angle (a or c, they’re interchangeable).
We know from linear pair theorem that b + 120° = 180°. So b = 60°
We can either use angle sum theorem or exterior angle theorem to find that last bad boy.
Angle sum theorem:
a + 60° + 30° = 180
a = 90°
Exterior angle theorem:
a + 30° = 120°
a = 90°
Step-by-step explanation:
Step-by-step explanation:
Exterior angle = 120° (given)
Interior opposite angles = 5 : 7
Let the common ratio be x.
So, interior opposite angles are 5x and 7x .
We know that,
By exterior angle property of a triangle
Exterior angle is equal to sum of interior opposite angles
⟹ 120° = 5x + 7x
⟹ 120° = 12x
⟹ 120°/12 = x
⟹ 10 =x
So, ∠ 1 = 5 × 10 = 50° ans.
So, ∠ 2 = 7 × 10 =120° ans