Question

Q12. One of the angles of a triangle is 84º and the remaining angles are in the ratio 1:5. Find the
measure of the remaining angles.
12​

Answer 1

Step-by-step explanation:

let angle 1= x°

angle 2 = 5x °

angle 3 = 84°

sum of all angles = 180°

x°+ 5x°+ 84° = 180

6x° = 180-84

6x °= 96

x° = 96÷6 = 16°

angle 1 = x = 16°

angle 2 = 5x = 5× 16 = 80°

angle 3 = 84°

Answer 2

Answer:

Measure of two remaining angles = 16°and 80°

Step-by-step explanation:

. Given :---

One angle of triangle = 84°

Two other angles are in ratio = 1:5

Let , two other angles are 1x ang 5x

. To Find :---

Measure of the angle which are 1x and 5x

. Explanation :---

Sum of interior angle of triangle = 180°

{here one interior angle is 84° and other two angles are 1x and 5x}

Therefore ,

84°+1x+5x = 180°

=> 84° + 6x = 180°

=> 6x = 180°- 84°

=> 6x = 96°

=> x = 96/6

=> x = 16°

Now, the value of x = 16°,

so, putting the value of x in 1x and 5x

===> 1x = 1×16 = 16°

===> 5x = 5×16 = 80°

so, the other two angles are = 16° and 80°

. Additional information about triangle:--

... Properties for triangle :

• Sum of interior angle of triangle is always 180°
• The sum of the length of the two sides of a triangle is greater than the length of the third side.
• the difference between the two sides of a triangle is less than the length of the third side.
• The side opposite the greater angle is the longest side of all the three sides of a triangle.
• The exterior angle of a triangle is always equal to the sum of the interior opposite angles. This property of a triangle is called an exterior angle property.
• Two triangles are said to be similar if their corresponding angles of both triangles are congruent and lengths of their sides are proportional.
• Area of a triangle = ½ × Base × Height
• The perimeter of a triangle = sum of all its three sides

.... Types of triangle :----

• Scalene Triangle: All the sides and angles are unequal.

• Isosceles Triangle: It has two equal sides. Also, the angles opposite these equal sides are equal.

• Equilateral Triangle: All the sides are equal and all the three angles equal to 60°.

• Acute Angled Triangle: A triangle having all its angles less than 90°.

• Right Angled Triangle: A triangle having one of the three angles exactly 90°.

• Obtuse Angled Triangle: A triangle having one of the three angles more than 90°.