Question

In a ∆ ABC , if ∠A=∠B=2C,Find each of the angles...please answers this question​

Answer 1

Step-by-step explanation:

In a ∆ ABC , if ∠A=∠B=2C,Find each of the angles...please answers this

Answer 2

Answer:

$\angle{A}$ = 72°

$\angle{B}$ = 72°

$\angle{C}$ = 36°

Step-by-step explanation:

Question:

In a ∆ ABC , if ∠A=∠B=2C, Find each of the angles...

Given:

• ∠A=∠B=2C

To find:

• Each of the angles

Angle sum property:

According to the Angle sum property:-

The sum of three angles of a triangle is 180°

That means, $\angle{A}$ + $\angle{B}$ + $\angle{C}$ = 180°

Solution:

Since, $\angle{A}$ = 2 $\times$ $\angle{C}$

$\angle{B}$ = 2 $\times$ $\angle{C}$

We need to substitute the value of Angle A and B as 2C in the following property:-

$\angle{A}$ + $\angle{B}$ + $\angle{C}$ = 180°

$2\angle{C}$ + $2\angle{C}$ + $\angle{C}$ = 180°

$5\angle{C}$ = 180°

$\angle{C}$ = $\dfrac{180}{5}$

$\angle{C}$ = 36°

Since $\angle{C}$ is 36°, $\angle{A}$ and $\angle{B}$ are:

$2\angle{C}$ = 2 $\times$ 36°

= 72°

Final answer:

$\angle{A}$ = 72°

$\angle{B}$ = 72°

$\angle{C}$ = 36°