All categories

3 years ago

What theorem or postulate can you use to determine a relationship between these two angles? Solve for x.

Mathematics

1 answer:

vfiekz [6]3 years ago

4 0

It's the consecutive interior angles theorem; it goes like this:

95° = (2x + 5)°
90° = 2x
45° = x

Basically it says the alternate interior angles of two parallel lines that are cut by a transverse line are equal/the same.

You might be interested in

Find cos(2*ABC) 100POINTS

juin [17]

Answer:

$-\dfrac{7}{25}$

Step-by-step explanation:

Trigonometric Identities

$\cos(A \pm B)=\cos A \cos B \mp \sin A \sin B$

Trigonometric ratios

$\sf \sin(\theta)=\dfrac{O}{H}\quad\cos(\theta)=\dfrac{A}{H}\quad\tan(\theta)=\dfrac{O}{A}$

where:

$\theta$ is the angle
O is the side opposite the angle
A is the side adjacent the angle
H is the hypotenuse (the side opposite the right angle)

Using the trig ratio formulas for cosine and sine:

$\cos(\angle ABC)=\dfrac{3}{5}$

$\sin(\angle ABC)=\dfrac{4}{5}$

Therefore, using the trig identities and ratios:

$\begin{aligned}\implies \cos(2 \cdot \angle ABC) & = \cos(\angle ABC + \angle ABC)\\\\& = \cos (\angle ABC) \cos (\angle ABC) - \sin(\angle ABC) \sin (\angle ABC)\\\\& = \cos^2(\angle ABC)-\sin^2(\angle ABC)\\\\& = \left(\dfrac{3}{5}\right)^2-\left(\dfrac{4}{5}\right)^2\\\\& = \dfrac{3^2}{5^2}-\dfrac{4^2}{5^2}\\\\& = \dfrac{9}{25}-\dfrac{16}{25}\\\\& = \dfrac{9-16}{25}\\\\& = -\dfrac{7}{25} \end{aligned}$

7 0

2 years ago

Read 2 more answers

Find the total surface area of a cube whose edge is 2 . 1 m

galben [10]

Answer:

Total surface of area =

$6l {}^{2}$

=6*2.1m

$12.6m ^{2}$

5 0

3 years ago

The answer to this.

Readme [11.4K]

Answer:

The two column proof is presented as follows;

Step ${}$ Statement Reason

1 ${}$ $\overline {AC}$ ≅ $\overline {BD}$ Given

${}$ ∠CAB ≅ ∠DBA

2 ${}$ $\overline {AB}$ ≅ $\overline {AB}$ Reflexive property

3 ${}$ ΔABC ≅ ΔBAD SAS rule of congruency

Step-by-step explanation:

Given that we have;

Segment $\overline {AC}$ of ΔABC being congruent to (≅) segment $\overline {BD}$ on ΔBAD and angle ∠CAB on ΔABC is congruent to angle ∠DBA on ΔBAD, and also that the two triangles share a common side, which is segment $\overline {AB}$ , we have;

Segment $\overline {AB}$ is congruent to itself by reflexive property, therefore;

Two sides and an included angle on ΔABC are congruent to the corresponding two sides and an included angle on ΔBAD, which by Side-Angle-Side, SAS, rule of congruency, ΔABC is congruent to ΔBAD

7 0

3 years ago

If y varies directly as x2 and y = 144 when x = 4, what is the value of y when x = -5?

muminat

Y varies with x² times a constant. We will call the constant a
144=ax²
144 = a(4²)
144 = 16a
a = 9
Apply our equation y = 9x²
y = 9(-5)²
y = 9* 25
y=225
Answer is B

6 0

3 years ago

3(12+b)=3•12+3•b

Olegator [25]

Distributive. The multiplication is distributed across the addition.

5 0

3 years ago