Question

Answer this, pretty Pleaseeeee.

I will mark the CORRECT answer as brainliest

Answer 1

$\setlength{\unitlength}{20} \begin{picture}( 0 , 0 ) \put(3 , 5){ \line( - 1 ,- 1){4}}\put( - 1 , 1){ \line( 1 , 0){10}}\put(7 , 1){ \vector(1 ,2){1.5}}\put(- 1 , 1){ \vector(1 ,2){2}}\put( 3 , 5){ \line(1 , - 1){4}}\qbezier(0.2 ,2)(0, 2.5)(- 0.3, 2.2)\qbezier(6.6,1.5)(7.7, 2)(8, 1)\put(3, 5.2){ \bf{A} }\put(- 1.5, 0.5){ \bf{B} } \put(7, 0.5){ \bf{C} }\put(0.1, 4){ \bf{P} } \put(8.7, 3){ \bf{Q} } \put( 0.1, 2.5){ \bf{20^{ \circ} } } \put(7, 1.8){ \bf{x} }\put(8, 1.2){ \bf{70^{ \circ} } } \end{picture}$

★ Given :

BP || CQ

AC = BC

★ To find:

measure of angle x

★ Solution :

AC = BC

therefore ,

Angle ABC = Angle BAC = y (assume)

We know that,

sum of all angles of triangles = 180°.

angle ABC + angle ACB + angle BAC = 180°

y+y + angle ACB = 180°

angle ACB = 180 - 2y

BP || CQ

We know that,

interior angles on same side of transversal are linear pairs.

→Angle PBC + Angle BCQ = 180° ..... (1)

angle PBC = 20° + y

Angle BCQ = angle ACB + x

= (180- 2y) +x

(20+y) + (180 - 2y+x) = 180

200 -y +x = 180

→ y - x = 20° .....(2)

We know that,

Exterior angle of a side = sum of other two interior angles .

In ∆ABC

70 + x = y+y

70+x = 2y

$\implies y = \frac{70+x}{2} ....(3)$

by putting value of y in equation 2

$\frac{70+x}{2} - x = 20 \\ \\ \\ \frac{70+x -2x}{2} = 20 \\ \\ \\ \frac{70-x}{2} = 20 \\ \\ \\ by\: cross\: multiplication\\ \\ \\ 70-x = 40 \\ \\ \\ x = 70-40$

$\bold{x = 30^{\circ}}$