Question

Amarjeet is studying in 9th class in Government school, Sandalpur Patna. Once he was at his home and was doing his geometry home work .He was trying to measure three angles of a triangle using the protractor, but his protractor was old and his protractor numbers were erased and the lines on the dee were visible. Let us help Amarjeet to find the angles of triangle.He found that the second angle of the triangle was four times as large as the first. The measure of the third angle is double of the first angle.
What was the value of the first angle ?

(a) 180◦ / 7

(b) 360 ◦ /7

(c) 720 ◦ /7

(d) None of these

What was the value of the second angle?(a) 180◦ / 7

(b) 360 ◦ /7

(c) 720 ◦ /7

(d) None of these

What was the value of the third angle?

(a) 180◦ / 7

(b) 360 ◦ /7

(c) 720 ◦ /7

(d) None of these

What was the value of <4 as shown in the figure?(a) 180◦ / 7

(b) 360 ◦ /7

(c) 720 ◦ /7

(d) None of these​

Answer 1

Answer:

first angle = 180/7

second angle = 720/7

third angle = 360/7

Step-by-step explanation:

there is not any figure to see the angle 4 sorry for angle also provide figure of that triangle

Answer 2

Given:

Measure of second angle = 4 × first angle

Measure of third angle = 2 × first angle

To find:

Measure of the first angle.

Measure of the second angle.

Measure of the third angle.

Solution:

In a triangle, the sum of all the angles equates to 180°.

Let $x$ be the measure of the first angle.

Then, the measure of the second angle = $4x$

Measure of the third angle = $2x$

By angle sum property of a triangle,

∠1 + ∠2 + ∠3 = 180°

$x+4x+2x=180$

$7x=180$

∴ $x=\frac{180}{7}$

Hence, the measure of the first angle is $\frac{180^{0}}{7}$. Hence, option (a) is correct.

Measure of the second angle = $4x=4*\frac{180}{7}=\frac{720^{0}}{7}$. Thus, option (c) is correct.

Measure of the third angle = $2x=2*\frac{180}{7}=\frac{360^{0}}{7}$. Thus, option (b) is correct.

The measure of the first angle is $\frac{180^{0}}{7}$. Option (a) is correct.

Measure of the second angle is $\frac{720^{0}}{7}$. Option (c) is correct.

Measure of the third angle is $\frac{360^{0}}{7}$. Option (b) is correct.