Question

in which activity is the use of a compass to draw circles and arcs particularly important? a. analyzing data b. solving equations c. constructing bisectors d. calculating volumes
in a triangle, an angle bisector divides the vertex angle into two equal angles, each measuring 2x + 12°. if the total vertex angle is 112°, what is the value of x? a. 22° b. 18° c. 25° d. 24°
why are perpendicular bisectors important when constructing a right angle? a. they form congruent triangles b. they ensure the creation of a 90 - degree angle c. they help in dividing angles into three equal parts d. they allow for precise measuring of side lengths
what role do right angles play in computer hardware design? a. structuring circuit board layouts b. reducing energy consumption c. increasing processing power d. enhancing aesthetic appeal

Explanation:

Step1: Analyze the first question

A compass is crucial for constructing bisectors as it helps in drawing circles and arcs which are used in the construction process. Analyzing data uses statistical methods, solving equations is algebraic, and calculating volumes involves formulas, none of which rely on compass - drawn circles/arcs like constructing bisectors.

Step2: Solve the second question

Since an angle bisector divides the vertex angle into two equal angles, and each angle measures \(2x + 12^{\circ}\) and the total vertex angle is \(112^{\circ}\), we can set up the equation \(2(2x + 12)=112\). First, expand the left - hand side: \(4x+24 = 112\). Then subtract 24 from both sides: \(4x=112 - 24=88\). Divide both sides by 4: \(x = 22\).

Step3: Analyze the third question

Perpendicular bisectors ensure the creation of a 90 - degree angle. They are used in geometric constructions to form right angles. They do not necessarily form congruent triangles in the context of creating a right angle, they don't divide angles into three equal parts, and they are not mainly for precise side - length measurement in the context of creating right angles.

Step4: Analyze the fourth question

Right angles play a role in structuring circuit board layouts in computer hardware design. They help in organizing components in an orderly and efficient manner. They do not reduce energy consumption, increase processing power, or change aesthetic appeal in the primary sense related to their geometric property in hardware design.

Answer:

1. c. Constructing bisectors
2. a. \(22^{\circ}\)
3. b. They ensure the creation of a 90 - degree angle
4. a. Structuring circuit board layouts