Question

please answer with brief explanation please all 5​

Answer 1

Step-by-step explanation:

Ans1

let x+y+w+z= 360°

now,

x+y+w+z=360°

=(w+z)+w+z=360° (because in Question,x+y=w+z)

=2(w+z) = 360°

=w+z= 360°/2=180°

Now, angle w = angle BOD

and,angle z = angle AOD

so, w+z = 180°

= AOD+BOD=180°

Hence, AOB is a line

Ans2

given:

ABC is an isosceles triangle.

AB=AC

to prove: angle b = angle c

now, if we draw AP perpendicular BC, BP and CP will be equal.

then, we will get two triangles, ABP and ACP

now,

ab= ac (given)

ap=ap (common)

bp=cp (proved above)

so, by SSS criteria ABP and ACP are equal.

Now by cpct, angle b is equal to angle c.

Ans3

let an angle x then, according to question,

x= a+b

now, we know that sum of interior angles of a triangle is 180°,

So,

x+a+b = 180°

=a+b+a+b= 180° (x=a+b is given)

=2(a+b) = 180°

=a+b = 180°/2

=a+b = 90°

So, x = a+b

=x = 90°

if one angle is 90° then the triangle is right angled triangle

Hence, it is right angled triangle.

Ans4

Given: QT is perpendicular to PR

TQR is 40° and SPR is 30°

to find: value of x and y

now, in triangle QTR

angle TQR+ angle QTR + angle TRQ= 180°

= 40° + 90° + TRQ = 180°

= 130° + TRQ

= TRQ = 180° - 130 °

= TRQ = 50°

= x = 50°

In triangle PSR, sum of two interior angles is equal to the opposite exterior angle,

So,

y = SPR+ x

y = 30° + 50°

y = 80°

Hence, x is 50° and y is 80°.

ans5

GIVEN: angle ABC is equal to angle ACB

and angle 3 is equal to angle 4.

(i) angle ABC = angle ACB

= angle ABC- angle 4 = angle ACB - angle 3

( because when equals are subtracted by equals then the remaining are equal)

= angle 1 = angle 2

(ii) angle ABC is equal to angle ACB

Hence, according to the theorem, if two angles are equal then there opposite sides will be equal,

So, AC = AB

Hence, justified that two sides of ABC are equal.

I hope that my solutions will be helpfull to you !