MATHEMATICS MIDDLE SCHOOL

Question 20. SQ is an angle bisector. Find the value of x. Please help!! Struggling

Answers

Answer 1

Answer:

Answer:

The value of x is 6.

Step-by-step explanation:

Given:

∠TSQ = (5x + 3)°

∠RSQ = (10x - 27)°

SQ is the angle bisector of ∠ TSR

To Find:

x = ?

Solution:

Angle Bisector:

A line that splits an angle into two equal angles.

'Bisect' means to divide into two equal parts.

SQ is the angle bisector of ∠ TSR ....Given

∴ $\angle TSQ=\angle RSQ$

Substituting the values we get

$(5x+3)=(10x-27)\n\n10x-5x=27+3\n\n5x=30\n\n\therefore x=(30)/(5)=6\n\therefore x=6$

The value of x is 6.

Given sum of fraction is:

$(9)/(10) + (5)/(6)$

To find: pair of fraction using least common denominator and summing equal to given sum of fraction.

Calculations:

Why do we need to find least common denominator?

It is because summing(or subtracting) fractions with common denominators is very easy as compared to those with unlike denominators.

When denominators are same, the sum or subtraction operation can directly work on the numerator values and their result will be putted on top of the denominator.

For example:

$(3)/(5) + (2)/(5) = (3+ 2)/(5) = (5)/(5) = 1$

The least common denominator of 10 and 6 is 30 since:

6 , 12, 18, 24, 30

10, 20, 30

The least number that is common in both 6's and 10's multiple's list is 30.

Rewriting both the fractions using least common denominator:

$(9)/(10) = (3 * 9)/(3 * 10) = (27)/(30)$

and

$(5)/(6) = (5 * 5)/(5 * 6) = (25)/(30)$

Since both the new fractions are of same value as of old pair, thus their sum would be same, as shown here:

$(9)/(10) + (5)/(6) = (27)/(30) + (25)/(30) = (52)/(30)$

Thus, the pair of fractions needed are $(27)/(30)$ and $(25)/(30)$ .

Learn more about fraction addition here:

brainly.com/question/17544795

Draw a 30° angle in standard position on the coordinate plane. Show the direction of rotation. Label the terminal side and the angle measure.

Answers

also the direction is anti clockwise

I hope it could help you :)

Final answer:

To draw a 30° angle in standard position on the coordinate plane, start by drawing the initial side of the angle which is the positive x-axis. Use a protractor to measure a 30° angle counterclockwise from the initial side. Then draw a line from the origin to the endpoint of the angle to represent the terminal side. Label the angle measure as 30° and label the terminal side accordingly. Indicate the direction of rotation by drawing an arrow showing the counterclockwise direction.

Explanation:

To draw a 30° angle in standard position on the coordinate plane, follow these steps:

Start by drawing the initial side of the angle, which is the positive x-axis.
Using a protractor, measure a 30° angle counterclockwise from the initial side.
Draw a line from the origin to the endpoint of the angle to represent the terminal side.
Label the angle measure as 30° and label the terminal side accordingly.
Indicate the direction of rotation by drawing an arrow showing the counterclockwise direction.