Question

please help me Q no.17 and 18​

Answer 1

Answer:

18)△ABC,

∠A=∠B+∠C

Now, sum of angles = 180

∠A+∠B+∠C=180

∠A+∠A=180

∠A=90

Thus, △ABC, is a right angled triangle.

Answer 2

Answer:

17.

Let ∆ABC be a triangle having all 3 angles of same measure.

According to the condition,

• angle ABC = angle BCA = angle CAB = x (let x be the value of all three angles)

Now, we know that,

• Sum of three angles of a triangle = 180°

So, ABC+BCA+CAB = 180°

=> x+x+x = 180°

=> 3x = 180°

=> x = 60°.

So, angle ABC = angle BCA = angle CAB = 60°

18.

Let ∆PQR be a triangle.

According to the condition,

• angle PQR = angle QRP + angle RPQ ... 1

Now, we know that,

Now, we know that,Sum of three angles of a triangle = 180°

So,

PQR + QRP + RPQ = 180°

=> PQR+(QRP + RPQ)= 180°

=> PQR+ PQR = 180°... from realtion 1

=> 2PQR = 180°

=> PQR = 90°

So, angle PQR of ∆ PQR is 90°

∆ PQR is a right- angled triangle.