The three angles of a triangle measure (2x-10°) , ( x + 31°) and ( 5x + 7°) . find the value of x and hence all the angles of the triangle.
Answers
Step-by-step explanation:
2x-10°+x+31°+5x+7°=180°
8x+28°=180°
8x=180°-28°
8x= 152
x=152 /8
x=19
(2x-10°)=2×19 -10 =28
(x+31°)=19+31=50
(5x+7°)=5×19+7=102
Given :-
- Three angles of a △ are :-
i.) (2x-10°)
ii.) (x+31°)
iii.) (5x+7°)
Now , refer to the attachment there is a figure of △ whose 3 angles measurement is given.
☆We know sum of three angles of a △ is 180°
Now, let's solve :-
(2x-10°) + (5x+7°) + (x+31°)
Removing the brackets,
→ 2x-10° + 5x+7° + x+31° = 180°
Now , pairing them that is taking all the x to one side and numbers to another side.
→ 2x° + 5x° + x° + 7° + 31° - 10° = 180°
→ 8x° + 28° = 180°
Now , taking positive 28 to right side from left side . So, it's sign will also change that is negative.
→ 8x° = 180° - 28°
→ 8x° = 152 °
→ x° = 152°/8°
→ x° = 19°
∴ Value of X is 19°
_________________________________
∴ Angles of three △ are :-
⓵ (2x - 10°)
→ 2(19)-10°
→38° - 10°
→ 28°
⓶ (x + 31°)
→ 19° + 31°
→ 50°
⓷ (5x+7°)
→ 5(19) +7°
→95 + 7°
→102°
∴ Value of X is 19° and the value of three angles of a △ is 28° , 50° , 102° .
More information :-
→ Triangle :--- is a plane figure with three straight sides and three angles.
→ Area of ∆ = 1/2 * Base * Height = 1/2* ab* sinC = 1/2 * bc *sinA = 1/2 * ca* sinB = √( s(s-a)(s-b)(s-c) ) [ where s = (a+b+c)/2 ]
→ There are three special names given to triangles that tell how many sides (or angles) are equal:---
1) Equilateral Triangle :-- Have Three equal sides and Three equal angles, always 60°..
2) Isosceles Triangle :-- Have Two equal sides and Two equal angles..
3) Scalene Triangle :-- No equal sides and No equal angles...
→ Triangles can also have names that tell you what type of angle is inside: ---
1) Acute Triangle = All angles are less than 90°..
2) Right Triangle = Has a right angle (90°)..
3) Obtuse Triangle = Has an angle more than 90°..
→ The three interior angles always add to 180°...
