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Let x = vertex angle Since all angles in a triangle add to 180 degrees, we know that 70+70+x = 180 140+x = 180 x = 180-140 x = 40 So the vertex angle is 40 degrees.
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Answer:
Step-by-step explanation:
A TRIANGLE is a polygon having 3 sides and 3 angles.
A REGULAR POLYGON is a polygon which all sides and all interior angles are equal.
There are 6 CLASSIFICATIONS OF TRIANGLES
1. Right Triangle
- has a 90 deg angle
2. Equilateral Triangle
- has 3 congruent sides and 3 congruent angles of which are 60 deg each.
3. Isosceles Triangle
- has 2 equal sides and angles.
4. Scalene Triangle
-All sides and angles are different from one another
5. Acute Triangle
-has one of its angles lesser than 90 deg.
6. Obtuse Triangle
-has one of its angles greater than 90 deg.
Recall that the SUM OF INTERIOR ANGLES of a triangle is equal to 180 deg.
In the above problem, it is stated that the triangle is isosceles. Therefore, its 2 sides and angles are equal, or its base angles are equal.
We assume A as the measure of each base angle, giving us 70 deg, A, and A as the angles. Adding all the angles and equating them to 180 deg, would give us
70 deg + A + A = 180 deg
Simplifying
70 deg + 2A = 180 deg
2A = 180 - 70
2A = 110
A = 55 deg
Therefore, each base angle measures 55 degrees.
Refer to the provided illustration for better understanding.
For more related problems, see links below.
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