Question

Answer all for brainliest asap pls

Answer 1

1.

Since ABCD is a rectangle, then

angleABE = 90 degrees

angle ABE + angle BEA + 41 = 180

Substitute the known and solve for angle BEA

angle BEA + 41 = 90

angle BEA = 49 degrees

But,

x + angleBEA + 61 = 180 (angles in a straight line)

x = 180 - 61 - 49

x = 70 degrees

2.

triangle XYZ is equilateral, meaning all angles in it are the same, each 60 degrees.

Therefore,

Angle YZX = 60

But Angle YZX = x + 32 (exterior angles equal to the sum of the two opposite interior angles)

60 = x + 32

Therefore,

x = 28 degrees

3.

Angle QPR = Angle QRP (equal oppo sides, equal opposite angles)

Therefore, 2angleQRP + 64 = 180 (angle sum of a triangle)

Angle QRP = 58 degrees

But angle QRP = x + 35 (exterior angles equal to the sum of the two opposite interior angles)

58 = x + 35

x = 23 degrees

Answer 2

Answer:

See below:

Step-by-step explanation:

For the first one, we know <ABC is 90 degrees due to it being a rectangle.

Since we know that, the angles in that triangle are 41 degrees 90 degrees and y degrees (y is <AEB) in this case.

We know that the sum of angles in a triangle are 180 degrees therefore:

If we solve that, we get that y is 49 degrees.

Now to get x, we know its a supplementary angle, therefore 61 degrees + 49 degrees + x = 180 degrees.

We now know that x is 70 degrees

For the second one, since its an equilateral triangle, we know that all angles inside of it are 60 degrees.

What we can do is first find what <XZW is by subtracting 60 from 180 due to the supplementary angles theorum.

Therefore <XZW is 120 degrees.

Now, all angles inside a triangle are always 180 degrees so therefore:

$x=180-(120+32)\\x=28$

For the final one, we know that <QRP is equal to 64 degrees due to the bottom two triangles of an isoceles triangle being equal.

On that, we get 23 degrees for the last one due to supplementary angles + 180 deg in triangle.