Question

Out of the following, the angle which is obtuse, is (a) 11 ⁄ 21 of a right angle (b) 11 ⁄ 21 of a straight angle (c) 8 ⁄ 20 of a straight angle (d) 8 ⁄ 20 of a right angle​

Answer 1

Answer:

11/21 is a obtuse angle yes

Answer 2

Given:

$\frac{11}{21}$ of a right angle, $\frac{11}{21}$ of a straight angle, $\frac{8}{20}$ of a straight angle, $\frac{8}{20}$ of a right angle.

To find:

An obtuse angle from the given options.

Solution:

A right angle is an angle having a measure of 90°.

A straight angle is an angle having measure of 180°.

An obtuse angle is an angle having measure more than 90°.

$\frac{11}{21}$ of a right angle means multiply 90 with $\frac{11}{21}$ to determine how much is the measure of that angle.

$\frac{11}{21}*90=47.14$

47.14° is less than 90°, so, it is definitely not an obtuse angle. Hence, option (a) is incorrect.

$\frac{11}{21}$ of a straight angle means, multiply 180 with $\frac{11}{21}$ to determine the measure of the angle.

$\frac{11}{21}*180=94.28$

94.28° is more than 90°. Therefore, it is an obtuse angle. Option (b) is the correct answer.

$\frac{8}{20}$ of a straight angle means, multiply 180 with $\frac{8}{20}$ to determine the measure of the angle.

$\frac{8}{20}*180=72$

72° is less than 90°. Hence, it is not an obtuse angle. Option (c) is incorrect.

$\frac{8}{20}$ of a right angle means multiply 90 with $\frac{8}{20}$ to determine the measure of the angle formed.

$\frac{8}{20}*90=36$

36° is less than 90°. Hence, it is not an obtuse angle. Option (d) is incorrect.

The only angle that gave a measure of more than 90° is $\frac{11}{21}$ of a straight angle. Hence, option (b) is the correct answer.

The other options are incorrect because they all produce results less than 90°.

$\frac{11}{21}$ of a straight angle is an obtuse angle. Option (b) is the correct answer.