Question

Find p, if the angles of a triangle have measures (p + 40°) , (2p + 20°) and 3p.

Answer 1

Answer:

Angle measures are:-

• P+20°=60°
• 2p+20°=60°
• 3p=60°

Step-by-step explanation:

Question:-

Find p, if the angles of a triangle have measures (p + 40°) , (2p + 20°) and 3p.

Given:-

Angles of triangle measuring P+40°,2p+20°,3p

To find:-

The measure of each a angle

Solution:-

Let us assume that

Angle 1=p+40°

Angle 2=2p+20°

Angle 3=3p

As the sum of three angle in a triangle is 180° it is also called as Angle sum property

According to the property we get,

angle 1+angle 2+angle 3=180°

On substituting the given values we get,

p+40°+2p+20°+3p=180°

Rearranging like terms,

P+2p+3p+40°+20°=180°

=>6p+60°=180°

=>6p=180°-60°

=>6p=120°

$=> \: p = \frac{120}{6}$

$\small\mathcal\pink{p=20°}$

$\huge\mathfrak\green{calculating \: the \: angles:-}$

P=20°

angle 1

P+20°

20°+40°

=60°

angle 2

2p+20°

2(20°)+20°

=>40°+20°

=>60°

angle 3

3p

3(20°)

=>60°

Verification:-

Sum of all angles in a triangle is 180°

Angle 1+angle 2+angle 3=180°(angle sum property)

On substituting the values we get,

60°+60°+60°=180°

180°=180°

Hence 180°=180°

Points to know:-

• In any triangle sum of all sides of a triangle is 180°.It is also called as angle sum property
• The each angle measure for equilateral triangle is 60°
• The base angles of isosceles triangle are equal
• The all three sides and angles of a scalene triangle is not equal
• In equilateral triangle always all three sides are equal
• In isosceles triangle always only two sides are equal

Additional information:-

Perimeter of equilateral triangle=3×side

Perimeter of scalene=Sum of all sides

Perimeter of isosceles triangle=Sum of all sides

Area of triangle=

$\frac{1}{2} \times base \times height$

Area of equilateral triangle=

$\frac{ \sqrt{3} }{4} ( {side}^{2} )$

Area of Scalene∆=

$\sqrt{s(s - a)(s - b)(s - c)}$

Where a, b and c are the sides

This is known as Heron's formula of triangle