Question

Guys please help...........................................................................

Answer 1

`\bold{\huge{\underline{ Solution }}}`

Given :-

• We have given two parallel lines and two lines intersecte each other and act as a transverse
• Due to the intersection between two parallel and two traverse lines a triangle is formed.
• The measurements of the given triangle are 60° , 20° and C

To Find :-

• We have to find the values of angles A, B and C

Let's Begin :-

Here, we have

• 1 triangle whose measures are 60° , 20° and C

Therefore,

By using Angle sum property

• ASP states that the sum of all angles of triangles are equal to 180°

That,

`\bold{\angle{X + }}{\bold{\angle{Y + }}}{\bold{\angle{Z = 180}}}{\degree}`

Subsitute the required values,

`\sf{ 60{\degree} + 20{\degree} + C = 180{\degree}}`

`\sf{ 80{\degree} + C = 180{\degree}}`

`\sf{ C = 180{\degree} - 80{\degree}}`

`\sf{ C = 100}{\degree}`

Thus, The value of C is 180°

Now,

We have to find the measurement of Angles A and B

Here,

• Angle B , unknown angle and Angle C lie on a straight line and we know that the angle formed by straight line is 180°
• Let the unknown angle be x which is equal to 20° ( Alternative interior angles)

Therefore,

`\sf{\angle{B + }}{\sf{\angle{ x + }}}{\sf{\angle{C = 180}}}{\degree}`

`\sf{\angle{ B + 20{\degree}+ 100{\degree} = 180{\degree}}}`

`\sf{\angle{ B + 20{\degree} = 180{\degree}- 100{\degree}}}`

`\sf{\angle{ B = 80{\degree} - 20{\degree}}}`

`\sf{\angle{ B = 60{\degree}}}`

Now,

• A, B and 100° lie on a straight line and we know that the angle formed by straight line is equal to 180°

Therefore ,

`\sf{\sf{A + }}{\sf{\angle{B + }}}{\sf{ 100{\degree} = 180}}{\degree}`

`\sf{\angle{ A + 60{\degree} = 180{\degree} - 100{\degree}}}`

`\sf{\angle{ A = 80{\degree} - 60{\degree}}}`

`\sf{\angle{ A = 20{\degree}}}`

Hence, The measure of Angles A, B and C are 20° , 60° and 100° .