Question

find angles x and y in each figure.

NCRTC class 7 ch-6
I want steps explanation
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Answer 1

Step-by-step explanation:

1. 120⁰+z( consider)=180⁰(linear pair of angles)

or, z=60⁰

y=z=60⁰(Angles opposite equal sides are equal)

x+y+z=180⁰(Angle sum property of a triangle?)

or, x+(60+60)⁰=180⁰

or, x+120⁰=180⁰

or, x=60⁰

2. Consider the angle with which y forms a linear pair as z.

Then,

x=z(Angles opposite equal sides are equal)

Notice that there is a right angle in the figure.

Consider the angle as p.

Then,

x+p+z=180⁰(Angle sum property of a triangle)

or,x+z+90⁰=180⁰

or,x+z=90⁰

x=z=45⁰(As they are equal)

Also, y+z=180⁰(linear pair of angles)

or, y+45⁰=180⁰

or,y=135⁰

3. Consider the angle to which the angle of measure 92⁰ is vertically opposite as z.

Then,

z=92⁰(vertically opposite angles)

Consider the angle with which y forms a linear pair as p.

Then,

x=p(Angles opposite equal sides are equal)

Also, x+p+z=180⁰

or, x+p=(180-92)⁰

or, x+p=88⁰

or, x=p=44⁰

Now, y+p=180⁰

or, y=(180-44)⁰

or, y=136⁰