Question

Maths questions:
1) The value of the supplement of the complement of 52° is :
2)If an angle is 146° greater than its supplement, then the measure of the angle is °.
3)If an angle is 13 /23 times its supplement, then that angle is °.
4)The sum of all the angles around a point is 180°. True or False
5)If the difference between the measure of an angle and its complement is 14°, find the measure of the angle.​

Answer 1

First of all, let us learn about Complementary angles and Supplementary angles.

Complementary angles:

Two angles $\angle A$ and $\angle B$ are called complementary if their sum is equal to $90^\circ$.

$\angle A + \angle B=90^\circ$

Complement of $\angle A = 90^\circ - \angle A$

Supplementary angles:

Two angles $\angle A$ and $\angle B$ are called supplementary if their sum is equal to $180^\circ$.

$\angle A + \angle B=180^\circ$

Supplement of $\angle A = 180^\circ - \angle A$

Now, let us solve the questions using above identities:

(1) To find supplement of complement of  $52^\circ$ = ?

Complement of $52^\circ$ = $90-52 =38^\circ$

Now taking supplement = 180 - 38 = $142^\circ$ is the answer.

(2) If an angle is 146° greater than its supplement, then the measure of the angle is °.

$\angle A = (180^\circ - \angle A) + 146^\circ\\\Rightarrow 2 \times \angle A = 326^\circ\\\Rightarrow \angle A = 163^\circ$

$163^\circ$ is the answer.

(3) If an angle is 13 /23 times its supplement, then that angle is °

$\angle A = \dfrac{13}{23} \times (180^\circ-\angle A)\\\Rightarrow 23\angle A = 13 \times 180 - 13\angle A\\\Rightarrow 36\angle A = 13 \times 180\\\Rightarrow \angle A = 65^\circ$

$65^\circ$ is the answer.

(4) The sum of all the angles around a point is 180°. True or False

The statement is false. Correct answer is 360°

(5) If the difference between the measure of an angle and its complement is 14°, find the measure of the angle.​

$\angle A - (90^\circ-\angle A ) = 14^\circ\\\Rightarrow 2\angle A = 14+90\\\Rightarrow 2\angle A = 104^\circ\\\Rightarrow \angle A = 52^\circ$

So, the answer is $52^\circ$

Answer 2

Given that,

Some questions

We know that,

Supplementary angle :

The addition of two supplement angle is equal to 180°.

$\angle A+\angle B=180^{\circ}$

Complementary angle :

The addition of two supplement angle is equal to 90°.

$\angle A+\angle B=90^{\circ}$

(1). The value of the supplement of the complement of 52° is

We need to calculate the complement angle

Using formula of complementary angle

$\angle A+\angle B=90^{\circ}$

$\angle B=90-\angle A$

Put the value into the formula

$\angle B=90-52$

$\angle B=38^{\circ}$

We need to calculate the supplement angle

Using formula of supplementary angle

$\angle A+\angle B=180^{\circ}$

$\angle B=180-\angle A$

Put the value into the formula

$\angle B=180-38$

$\angle B=142^{\circ}$

(2). If an angle is 146° greater than its supplement, then the measure of the angle is

If the angle is x.

The supplement angle is (x+146)

We need to calculate the supplement angle

Using formula of supplementary angle

$\angle A+\angle B=180^{\circ}$

Put the value into the formula

$x+(x+146)=180$

$2x=180-146$

$x=\dfrac{180-146}{2}$

$x=17^{\circ}$

The supplement angle is

$\angle B = x+146$

Put the value of x

$\angle B = 17+146$

$\angle B = 163^{\circ}$

(3). If an angle is 13 /23 times its supplement, then that angle is

If the angle is x.

The supplement angle is $x\times\dfrac{13}{23}$

We need to calculate the supplement angle

Using formula of supplementary angle

$\angle A+\angle B=180^{\circ}$

Put the value into the formula

$x+(x\times\dfrac{13}{23})=180$

$\dfrac{23x+13x}{23}=180$

$x=\dfrac{180\times23}{36}$

$x=115^{\circ}$

The supplement angle is

$\angle B = x\times\dfrac{13}{23}$

Put the value of x

$\angle B = 115\times\dfrac{13}{23}$

$\angle B= 65^{\circ}$

(4). The sum of all the angles around a point is 180°.

We know that,

The sum of all the angles around a point is 360°.

So, given statement is false.

(5). If the difference between the measure of an angle and its complement is 14°, find the measure of the angle.​

We need to calculate the angle

Using given data

$\angle A-(90-\angle A)=14$

$2\angle A=90+14$

$\angle A=\dfrac{104}{2}$

$\angle A=52^{\circ}$

Hence, (1). The angle is 142°

(2). The angle is 163°

(3). The angle is 65°

(4). false

(5). The angle is 52°