angles and triangles homework 1

Chapter 1: Triangles and Circles

Exercises: 1.1 Triangles and Angles

Practice each skill in the Homework Problems listed.

Sketch a triangle with given properties #1–6
Find an unknown angle in a triangle #7–12, 17–20
Find angles formed by parallel lines and a transversal #13–16, 35–44
Find exterior angles of a triangle #21–24
Find angles in isosceles, equilateral, and right triangles #25–34
State reasons for conclusions #45–48

Exercises for 1.1 Triangles and Angles

Exercise group, 1. an isosceles triangle with a vertex angle [latex]306^{\circ}[/latex], 2. a scalene triangle with one obtuse angle ( scalene means three unequal sides.), 3. a right triangle with legs [latex]4[/latex] and [latex]7[/latex], 4. an isosceles right triangle, 5. an isosceles triangle with one obtuse angle, 6. a right triangle with one angle [latex]20°[/latex].

In parts (a) and (b), find the exterior angle [latex]\phi[/latex].

Use your answer to part (c) to write a rule for finding an exterior angle of a triangle.

In Problems 25 and 26, the figures inscribed are regular polygons , which means that all their sides are the same length, and all the angles have the same measure. Find the angles [latex]\theta[/latex] and [latex]\phi[/latex].

In problems 27 and 28, triangle ABC is equilateral. Find the unknown angles.

a. [latex]2\theta + 2\phi =[/latex]

b. [latex]\theta + \phi =[/latex]

c. [latex]\triangle ABC[/latex] is

Find [latex]\alpha[/latex] and [latex]\beta[/latex]

Explain why [latex]\angle OAB[/latex] and [latex]\angle ABO[/latex] are equal in measure.
Explain why [latex]\angle OBC[/latex] and [latex]\angle BCO[/latex] are equal in measure.
Explain why [latex]\angle ABC[/latex] is a right angle. (Hint: Use Problem 29.)
Compare [latex]\theta[/latex] with [latex]\alpha + \beta[/latex] (Hint: What do you know about supplementary angles and the sum of angles in a triangle?)
Compare [latex]\alpha[/latex] and [latex]\beta[/latex]
Explain why the inscribed angle [latex]\angle BAO[/latex] is half the size of the central angle [latex]\angle BOD[/latex]

Find [latex]\alpha[/latex] and [latex]\beta[/latex]

[latex]\angle 4 + \angle 2 + \angle 5 =[/latex]
Use parts (a) and (b) to explain why the sum of the angles of a triangle is [latex]180^{\circ}[/latex]

ABCD is a rectangle. The diagonals of a rectangle bisect each other. In the figure, [latex]\angle AQD = 130^{\circ}[/latex]. Find the angles labeled 1 through 5 in order, and give a reason for each answer.

A tangent meets the radius of a circle at a right angle. In the figure, [latex]\angle AOB = 140^{\circ}[/latex]. Find the angles labeled 1 through 5 in order, and give a reason for each answer.