Mathematics

# Two angles of a triangle are equal and the third angle is greater than each one of them by $18^{\circ}$. Find the angles.

##### SOLUTION
Consider $\angle A$ and $\angle B$ in a triangle is $x^{\circ}$

We know that the sum of all the angles in a triangle is $180^{\circ}$.

So we can write it as

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

By substituting the values

$x^{\circ} + x^{\circ} + \angle C = 180^{\circ}$

By addition

$2x^{\circ} + \angle C = 180^{\circ} .. (1)$

According to the question we get

$\angle C = x^{\circ} + 18^{\circ} . (2)$

By substituting (2) in (1) we get

$2x^{\circ} + x^{\circ} + 18^{\circ} = 180^{\circ}$

On further calculation

$3x^{\circ} + 18^{\circ} = 180^{\circ}$

By subtraction

$3x^{\circ} = 180^{\circ} - 18^{\circ}$

$3x^{\circ} = 162^{\circ}$

By division

$x^{\circ} = 162/3$

$x^{\circ} = 54^{\circ}$

By substituting the values of $x$

$\angle A = \angle B = 54^{\circ}$

$\angle C = 54^{\circ} + 18^{\circ} = 72^{\circ}$

Therefore, $\angle A = 54^{\circ}, \angle B = 54^{\circ}$ and $\angle C = 72^{\circ}$.

You're just one step away

Create your Digital Resume For FREE on your name's sub domain "yourname.wcard.io". Register Here!

Subjective Medium Published on 09th 09, 2020
Questions 120418
Subjects 10
Chapters 88
Enrolled Students 86

#### Realted Questions

Q1 Single Correct Medium
In the given figure, $\angle AOB={ 90 }^{ o }$ and $COD$ is a straight line. The values of $x$ and $y$ are respectively.
• A. ${25}^{o}$ and ${15}^{o}$
• B. ${15}^{o}$ and ${45}^{o}$
• C. ${10}^{o}$ and ${60}^{o}$
• D. ${20}^{o}$ and ${30}^{o}$

Asked in: Mathematics - Lines and Angles

1 Verified Answer | Published on 09th 09, 2020

Q2 Single Correct Medium
The equation of a straight line passing through the point $(2,-7)$ and parallel to x-axis is
• A. $x=2$
• B. $x=-7$
• C. $y=2$
• D. $y=-7$

Asked in: Mathematics - Lines and Angles

1 Verified Answer | Published on 09th 09, 2020

Q3 Single Correct Medium
The difference between the supplement of an angle and the angle is $36^{\circ}$. The supplement is:
• A. $72^{\circ}$
• B. $63^{\circ}$
• C. $27^{\circ}$
• D. $108^{\circ}$

Asked in: Mathematics - Lines and Angles

1 Verified Answer | Published on 09th 09, 2020

Q4 One Word Medium
Find complementary angle of $23^{\circ}$.

Asked in: Mathematics - Lines and Angles

1 Verified Answer | Published on 09th 09, 2020

Q5 Subjective Medium
Classify the following angle as right, straight, acute, obtuse or reflex.

Asked in: Mathematics - Lines and Angles

1 Verified Answer | Published on 09th 09, 2020