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Leto [7]
2 years ago
8

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

Mathematics
1 answer:
djverab [1.8K]2 years ago
7 0

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

<h3><u>Given </u><u>:</u><u>-</u></h3>

  • 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

<h3><u>To </u><u>Find </u><u>:</u><u>-</u></h3>

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

<h3><u>Let's </u><u>Begin </u><u>:</u><u>-</u></h3>

<u>Here</u><u>, </u><u> </u><u>we </u><u>have </u>

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

<h3><u>Therefore</u><u>, </u></h3>

By using Angle sum property

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

<u>That</u><u>, </u>

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

<u>Subsitute</u><u> </u><u>the </u><u>required </u><u>values</u><u>, </u>

\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°

<h3><u>Now</u><u>, </u></h3>

We have to find the measurement of Angles A and B

<u>Here</u><u>, </u>

  • 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)

<h3><u>Therefore</u><u>, </u></h3>

\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}}}

<h3><u>Now</u><u>, </u></h3>

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

<h3><u>Therefore </u><u>,</u></h3>

\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° .

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