Solve the following geometry problems involving angles and their definitions, including constructing a…

Question

Solve the following geometry problems involving angles and their definitions, including constructing a 90-degree angle.

ScanSolve AI Tutor · Accepted Answer

Here are the solutions to the questions:

9. Answer the following question

a) Define acute angle.
An acute angle is an angle that measures greater than $0^\circ$ but less than $90^\circ$ .

b) Write the name of the angle formed in the straight line.
The angle formed by a straight line is called a straight angle. It measures $\boxed{180^\circ}$ .

c) What is the straight line?
A straight line is a one-dimensional figure that extends infinitely in both directions without any curve. It is the shortest distance between any two points on it.

d) Find the value of x.

Identify the angles on the straight line AB.
From the diagram, we have an angle of $120^\circ$ and an angle $x$ on the straight line AB.
Recall that angles on a straight line sum to $180^\circ$ .
$x + 120^\circ = 180^\circ$
Solve for $x$ .
$x = 180^\circ - 120^\circ$ $x = 60^\circ$
The value of $x$ is $\boxed{60^\circ}$ .

e) Construct the following angle by using compass and pencil.

a) $90^\circ$
Draw a line segment AB and mark a point O on it.
With O as the center, draw an arc of any convenient radius that intersects AB at two points, say P and Q.
With P and Q as centers, and a radius greater than OP, draw two arcs that intersect each other above (or below) AB at a point, say R.
Draw a line segment from O to R.
The angle $\angle AOR$ (or $\angle BOR$ ) is $\boxed{90^\circ}$ .

b) $30^\circ$
Draw a line segment AB and mark a point O on it.
With O as the center, draw an arc of any convenient radius that intersects AB at a point, say P.
With P as the center and the same radius, draw another arc that intersects the first arc at a point, say Q.
The angle $\angle QOP$ is $60^\circ$ .
Now, bisect the $60^\circ$ angle.
With P and Q as centers, and a radius greater than half the distance PQ, draw two arcs that intersect each other at a point, say R.
Draw a line segment from O to R.
The angle $\angle ROP$ is $\boxed{30^\circ}$ .

Solve the following geometry problems involving angles and their definitions, including constructing a 90-degree angle.

Step-by-step solution

Identify the angles on the straight line AB.

Recall that angles on a straight line sum to $180^\circ$ .

Solve for $x$ .

Draw a line segment AB and mark a point O on it.

With O as the center, draw an arc of any convenient radius that intersects AB at two points, say P and Q.

With P and Q as centers, and a radius greater than OP, draw two arcs that intersect each other above (or below) AB at a point, say R.

Draw a line segment from O to R.

Draw a line segment AB and mark a point O on it.

With O as the center, draw an arc of any convenient radius that intersects AB at a point, say P.

With P as the center and the same radius, draw another arc that intersects the first arc at a point, say Q.

Now, bisect the $60^\circ$ angle.

Draw a line segment from O to R.

Still stuck on this one?

More Mathematics Questions

Solve the following geometry problems involving angles and their definitions, including constructing a 90-degree angle.

Step-by-step solution

Identify the angles on the straight line AB.

Recall that angles on a straight line sum to 180∘180^\circ180∘.

Solve for xxx.

Draw a line segment AB and mark a point O on it.

With O as the center, draw an arc of any convenient radius that intersects AB at two points, say P and Q.

With P and Q as centers, and a radius greater than OP, draw two arcs that intersect each other above (or below) AB at a point, say R.

Draw a line segment from O to R.

Draw a line segment AB and mark a point O on it.

With O as the center, draw an arc of any convenient radius that intersects AB at a point, say P.

With P as the center and the same radius, draw another arc that intersects the first arc at a point, say Q.

Now, bisect the 60∘60^\circ60∘ angle.

Draw a line segment from O to R.

Still stuck on this one?

More Mathematics Questions

Recall that angles on a straight line sum to $180^\circ$ .

Solve for $x$ .

Now, bisect the $60^\circ$ angle.