Angle measures and segment lengths. Algebra Find the value of each variable.

Mathematics

1 answer:

Katyanochek1 [597]3 years ago

6 0

(9)

x ° = 1/2 (130° - 30°) = 50°

(due to a theorem about intersecting secants/tangents)

(11) The labeled angle subtends a minor arc of meaure 120°, which means the larger arc has a measure of 360° - 120° = 240°. Then

x ° = 1/2 (240° - 120°) = 60°

(due to the same theorem)

(13) The labeling here is a bit confusing. I'm not sure what the 70° is referring to. It occurs to me that it might be info from a different exercise, so that y ° is the measure of the angle made by the tangent to the circle with a vertex of the pentagon, and x ° is the measure of each arc that passes over an edge of the pentagon.

Each arc makes up 1/5 of the circle's circumferece, so

x ° = 360°/5 = 72°

The pentagon is regular, so each of its interior angles have the same measure of 108°. (Why 108°? Each exterior angle measures 360°/5 = 72°, since the exterior angles sum to 360°. Interior and exterior angles are supplementary, so the interior angles measure 180° - 72° = 108° each.)

The angles formed by the tangent to the circle are supplementary, so that

y ° + 108° + y ° = 180°

2y ° = 72°

y ° = 36°

You might be interested in

If R is the set of all integers with absolute value less than 10, A is its subset containing all natural numbers less than 10 an

Elza [17]

Answer:

See explanation

Step-by-step explanation:

1. R is the set of all integers with absolute value less than 10, thus

$R=\{a\in \mathbb{Z}\ :\ |a|$

2. A is its subset containing all natural numbers less than 10, thus

$A\subset R\\ \\A=\{b\in \mathbb{N}\ :\ b$

3. B is the set of all integer solutions of inequality 2x+5<9 that are less than 10 by absolute value (and therefore, it is also a subset of R). First, solve the inequality:

$2x+5$