if the angle of a triangle are in the ratio 1:2:1 , find all the angle of the triangle classify the triangle in two different ways
Answers
Step-by-step explanation:
the triangle is isosceles triangle ️ so measures of triangle are
1x +2x +1x = 180 degree
4x = 180
x= 180/4
x = 45
1x = 45
2x = 45 x 2
= 90
so, the measures of triangle are 45, 90 , 45,
.
. . 45, 90, 45 = 1:2:1
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Given :-
- Ratio of the angles of triangle = 1 : 2 : 1
To find :-
- All the angles of triangle and classify the triangle in two different ways.
Knowledge Required :-
• Formula to calculate sum of interior angles of a polygon.
- Sum of interior angles of a polygon = (2n - 4) × 90°
where,
- n = number of sides of the polygon
Solution :-
Let the angles of triangle be x, 2x and x.
- First angle = x
- Second angle = 2x
- Third angle = x
Triangle has 3 sides, 3 angles.
Number of sides (n) = 3
→ x + 2x + x = (2n - 4) × 90°
→ 4x = ((2 × 3) - 4) × 90°
→ 4x = (6 - 4) × 90°
→ 4x = 2 × 90°
→ 4x = 180°
→ x = 180°/4
→ x = 45°
The value of x = 45°
Substitute the value of x in the angles of triangle.
→ First angle = x = 45°
→ Second angle = 2x = 2 × 45° = 90°
→ Third angle = x = 45°
- Therefore, the three angles of triangle are 45°, 90° and 45°.
The triangle is an Isosceles triangle because two angles are equal to each other and third angle is unequal and also it is a right - angled triangle as one of the angle is 90°.
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Verification :-
Add all the three angles of triangle if their sum is equal to 180°, then the values are right.
→ 45° + 90° + 45°
→ 180°
Sum of angles of triangle = 180°.
Hence, verified