Answer:
see the explanation
Step-by-step explanation:
we know that
A shape with two opposite angles equal to 105° could be a quadrilateral, a parallelogram, a rhombus or a trapezoid
Because
<em>A quadrilateral</em>: A quadrilateral is a four-sided polygon. The sum of the interior angles in any quadrilateral must be equal to 360 degrees
so
If the quadrilateral have two opposite angles equal to 105°, then the sum of the other two interior angles must be equal to

<em>A parallelogram</em>: A Parallelogram is a flat shape with opposite sides parallel and equal in length. Opposite angles are congruent and consecutive angles are supplementary
so
If the parallelogram have two opposite angles equal to 105°, then the measure of each of the other two congruent interior angles must be equal to

<em>A rhombus</em>: A Rhombus is a flat shape with 4 equal straight sides. A rhombus looks like a diamond. All sides have equal length. Opposite sides are parallel. Opposite angles are congruent and consecutive angles are supplementary
so
If the Rhombus have two opposite angles equal to 105°, then the measure of each of the other two congruent interior angles must be equal to

<em>A trapezoid</em>: A trapezoid is a 4-sided flat shape with straight sides that has a pair of opposite sides parallel
so
If the trapezoid have two opposite angles equal to 105°, then the sum of the other two interior angles must be equal to

9514 1404 393
Answer:
(d) Infinitely Many Solutions
Step-by-step explanation:
Each point of intersection between the lines is a solution. When the lines lie on top of each other, there are infinitely many points of intersection, hence ...
Infinitely Many Solutions
Answer:
D) 50
20/0.4=50
Step-by-step explanation:
Answer:
- b/a
- 16a²b²
- n¹⁰/(16m⁶)
- y⁸/x¹⁰
- m⁷n³n/m
Step-by-step explanation:
These problems make use of three rules of exponents:

In general, you can work the problem by using these rules to compute the exponents of each of the variables (or constants), then arrange the expression so all exponents are positive. (The last problem is slightly different.)
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1. There are no "a" variables in the numerator, and the denominator "a" has a positive exponent (1), so we can leave it alone. The exponent of "b" is the difference of numerator and denominator exponents, according to the above rules.

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2. 1 to any power is still 1. The outer exponent can be "distributed" to each of the terms inside parentheses, then exponents can be made positive by shifting from denominator to numerator.

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3. One way to work this one is to simplify the inside of the parentheses before applying the outside exponent.

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4. This works the same way the previous problem does.

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5. In this problem, you're only asked to eliminate the one negative exponent. That is done by moving the factor to the numerator, changing the sign of the exponent.

Answer:
Part 1) m∠1 =(1/2)[arc SP+arc QR]
Part 2) 
Part 3) PQ=PR
Part 4) m∠QPT=(1/2)[arc QT-arc QS]
Step-by-step explanation:
Part 1)
we know that
The measure of the inner angle is the semi-sum of the arcs comprising it and its opposite.
we have
m∠1 -----> is the inner angle
The arcs that comprise it and its opposite are arc SP and arc QR
so
m∠1 =(1/2)[arc SP+arc QR]
Part 2)
we know that
The <u>Intersecting Secant-Tangent Theorem,</u> states that the square of the measure of the tangent segment is equal to the product of the measures of the secant segment and its external secant segment.
so
In this problem we have that

Part 3)
we know that
The <u>Tangent-Tangent Theorem</u> states that if from one external point, two tangents are drawn to a circle then they have equal tangent segments
so
In this problem
PQ=PR
Part 4)
we know that
The measurement of the outer angle is the semi-difference of the arcs it encompasses.
In this problem
m∠QPT -----> is the outer angle
The arcs that it encompasses are arc QT and arc QS
therefore
m∠QPT=(1/2)[arc QT-arc QS]