Question

Find two vertical angles such that the first angle is 15 less than 4 times the second angle.

Answer 1

Answer:

First vertical angle = 141°

Second vertical angles = 39°

Step-by-step explanation:

If two lines intersect each other, then the opposite angles are called vertical angles. Lines make two pairs of vertical angles.

We need to find two vertical angles such that the first angle is 15 less than 4 times the second angle.

Let x be the measure of second angle.

Measure of first angle = 4x-15.

The sum of two vertical angles is 180° because they are linear pair.

$x+(4x-15)=180$

$5x-15=180$

Add 15 on both sides.

$5x-15+15=180+15$

$5x=195$

Divide both sides by 5.

$x=\frac{195}{5}$

$x=39$

The value of x is 39. It means the measure of second vertical angles is 39°.

Measure of first angle = $4x-15=4(39)-15=141^{\circ}$

Therefore, the measure of first angle is 141°.