Question

Please moderators help me.
Find rest all angles.

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I will report ​

Answer 1

Answer:

∠ M = 75°

∠N = 105°

Step-by-step explanation:

∠M and 105° are on the same line. They are in linear pair form

We know that, linear pair means sum of both angle gives 180°

Diagram :

$\setlength{\unitlength}{1 cm}\begin{picture}(0,0)\thicklines\put(5,1){\vector(1,0){4}}\put(5,1){\vector(-1,0){4}}\put(5,1){\vector(1,1){3}}\put(2,2){ \underline{\boxed{\large\sf a + b = 180^{\circ}} }}\put(4.5,1.3){ \sf a^{\circ} }\put(5.7,1.3){ \sf b^{\circ} }\end{picture}$

So, as these are in linear pair

=> M + 105° = 180°

=> ∠M = 75°

_____________________

Now finding N,

105° and ∠N are on the opposite sides of the transversal line passing through the 2 parallel lines.

We know that, these are called as alternate angles and these angles are equal.

Diagram :

$\setlength{\unitlength}{1cm}\begin{picture}(0,0)\thicklines\multiput(0,0)(0,3){2}{\line(1,0){4}}\qbezier(0,0)(0,0)(4,3)\qbezier(1,0)(1.2,0.35)(0.8,0.6)\qbezier(3,3)(2.8,2.65)(3.2,2.4)\put(2.5,0.02){\vector(1,0){0}}\put(1.5,3.02){\vector(-1,0){0}}\end{picture}$

So, ∠N = 105°

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Hope it helps!!