Question

6. Find 'x' in the following figures . pls solve both the figures ..... ​

Answer 1

$\huge\bold{\gray{\sf{Answer:}}}$

Explanation:

$\huge\bold{\pink{a)}}$

In ∆ABC

∠A+∠B+∠C=180°$\bold{\red{(by \:angle \:sum\: property)}}$

$= > 65 + 45 + x = 180$

$= > 110 + x = 180$

$= > x = 180 - 110 = 70$

Hence,the first angle which is ∠A is 70°

$\huge\bold{\pink{b)}}$

40°=∠A (vertically opposite angle)

∠B=∠C(equal sides have equal angle)

so,∠B=∠C='x'

Now adding all three angles :

=>∠A+∠B+∠C=180°

=>40°+x+x=180°

=>40°+2x=180°

=>2x=180°-40°=140°

$2x = 140°$

$\bold{\purple{x= 70°}}$

Therefore,∠A=40°

ㅤㅤㅤㅤㅤ∠B=∠C=70°

Answer 2

Answer:

Figure 1. Answer is 70°

Figure 2. Answer is 70°

Step-by-step explanation:

Figure 1.

Sum of all angles of triangle is 180°

So

65°+45°+ x = 180°

110° + X =180°

Transferring 110° to RHS

x = 180°-110°

x= 70°

Figure 2.

Since, Angle A is 40°

So , Angle BAC is also of 40 ° (vertically opposite angle)

Since, AB=AC

So, Angle B=Angle C ( Angle opposite to the equal sides of a triangle is always equal)

So , both angles be 2x

Since, Sum of all sides of triangle is 180°

So, 40° + 2x = 180°

(Transferring 40° to RHS)

2x=180°-40°

2x= 140°

(Transferring 2 To RHS )

x= 140°/2

x=70°

Hope It Will Help You

Thank U