Question

Bryce drew a rectangle and labeled five of the angles, as shown. He knew these factsWHOabout the angles:• The measurements of angles 1 and 3 are the same.The measurement of angle 2 equals 110°.• The measurements of angles 3 and 5 are the same.Part A Based on these facts, what is the sum of the measurements of angle 1and angle 2? Show your work or explain your answer.Part B What is the measurement of angle 4? Show your work or explain your answer.

Answer 1

The given figure is;

It is given that :

The measurements of angles 1 and 3 are the same.

The measurement of angle 2 equals 110°.

PART A:

Since, angle 1 , 2 and 3 are lie at the same point on the same line

Thus, from the property of angle on a line

Sum of all angles on a strainght line at a point is equal to 180 degree

thus;

Angle1 + Angle2 + Angle 3 = 180

Angle 1 + Angle 2 + Angle1 = 180 {Angle1 = Angle 3, given}

2(Angle 1) + Angle 2 = 180

2 (angle 1) + 110 = 180 {Angle 2 = 110, given}

2(Angle 1) = 180 -110

2(Angle 1) = 70

Angle 1 = 70/2

Angle 1 = 35

Since, angle 2 = 110

The sum of angle 1 and 2 is 110 + 35

Sum of angle 1 and 2 = 145

PART B:

From the properties of the rectangle;

All the angles of a rectangle are 90°

In the given rectangle;

Thus, in the triangle form by the angle3, 4 and the right angle

Sum of all angles in a triangle is equal to 180

Angle 3 + Angle 4 + 90 = 180

35 + Angle 4 + 90 = 180

Angle 4 + 125 = 180

Angle 4 = 180 - 125

Angle 4 = 55

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