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Phone Plan Screen Angles

Use angle relationships to check a phone plan comparison screen.

Answer Key

Triangular Plan Tags

A design team is building a screen that compares phone and data plans. Check the triangular tags used to highlight plans. Angle measures are in degrees.

1.
A triangular “No Contract” tag has two interior angles measuring 43° and 76°.

What is the measure of its third interior angle? 61°

2.
A triangular data-plan tag has interior angles of 48° and 67° at two vertices. A side is extended at the third vertex. Which statement correctly finds the exterior angle there?
  • A. The exterior angle is 19° because 67 − 48 = 19.
  • B. The exterior angle is 65° because 180 − (48 + 67) = 65.
  • C. The exterior angle is 115° because 48 + 67 = 115.
  • D. The exterior angle is 132° because 180 − 48 = 132.
3.
At one corner of a triangular tag, an interior angle x and its adjacent exterior angle form the straight angle shown.128°x

What is the measure of x? 52°

4.
A triangular “Extra Data” tag has interior angles measuring x°, 2x°, and 3x°.

Find x. 30

5.
To explain the triangle angle sum, Jada draws a line through the top vertex of a triangular tag parallel to its base. The two base angles equal two angles at the top by alternate interior angles. What completes her argument?
  • A. The three angles at the top form a full turn, so their sum is 360°.
  • B. The three angles at the top form a straight angle, so their sum is 180°.
  • C. The two copied angles alone form a straight angle, so their sum is 180°.
  • D. The three angles at the top form a right angle, so their sum is 90°.

Parallel Screen Dividers

The comparison screen has two parallel horizontal divider lines. A straight diagonal accent crosses both lines, rising from left to right. Use this layout for Questions 6–9.

6.
The angle above the upper divider and to the right of the diagonal measures 62°. Which statement about the angle above the lower divider and to the right of the diagonal is correct?
  • A. It measures 62° because corresponding angles are equal.
  • B. It measures 62° because the two angles are vertical angles.
  • C. It measures 118° because corresponding angles are supplementary.
  • D. It measures 118° because alternate interior angles are supplementary.
7.
The angle above the upper divider and to the right of the diagonal measures 62°.

What is the measure of the angle above the lower divider and to the left of the diagonal? 118°

8.
In a revised layout, the angle below the upper divider and to the right of the diagonal measures (3x + 8)°. The angle above the lower divider and to the right of the diagonal measures (2x + 17)°. These are same-side interior angles.

Find x. 31

9.
Select every statement that must be true for the two parallel dividers and the diagonal accent.

Alternate interior angles have equal measures.All eight angles at the two intersections have equal measures.Same-side interior angles have a sum of 180°.Corresponding angles always have a sum of 180°.

10.
A new triangular plan tag has remote interior angles of 34° and 79° relative to an exterior angle e. Luis writes e = 79 − 34. Which argument correctly repairs his work?
  • A. The third interior angle is 67°, and e + 67 = 180, so e = 113°.
  • B. The third interior angle is 67°, and e = 67, so e = 67°.
  • C. The exterior angle supplements 34°, and e + 34 = 180, so e = 146°.
  • D. The exterior angle supplements 79°, and e + 79 = 180, so e = 101°.

Graphics for Different Screen Sizes

Use angle relationships to decide whether triangular graphics have the same shape. Similar triangles may have different sizes.

11.
Two versions of a triangular plan icon have the angle measures shown. Which conclusion is justified?
Plan Icon Versions
VersionKnown angleKnown angle
Compact41°72°
Expanded72°67°
  • A. They cannot be compared unless all side lengths are provided.
  • B. They are not similar because the two listed angle pairs differ.
  • C. They must be the same size because both contain a 72° angle.
  • D. They are similar because both have angles of 41°, 67°, and 72°.
12.
Each item lists two interior angles of a triangular plan badge. Match it to the badge with a similar shape in the right column.
  1. Starter badge: 37° and 58°C
  2. Shared badge: 46° and 63°B
  3. Unlimited badge: 52° and 57°A
  1. A. A badge with angles of 57° and 71°
  2. B. A badge with angles of 63° and 71°
  3. C. A badge with angles of 58° and 85°
13.
A triangular plan graphic is labeled ABC. Point D lies on side AB, and point E lies on side AC. Segment DE is parallel to BC. Angle BAC measures 46°, and angle ABC measures 61°. The smaller triangle ADE will be used as a phone notification icon.

What is the measure of angle AED? 73°

14.
Two triangular plan icons each have angles of 44° and 81°. Noor says, “The icons must have the same shape and the same size.” Explain which part of Noor’s claim is justified and which part is not. Use the triangle angle sum and angle-angle similarity in your reasoning.

Each third angle is 180 − 44 − 81 = 55°. The triangles have matching angles, so AA similarity guarantees the same shape. It does not guarantee the same size: one icon could be an enlargement of the other, with all side lengths doubled.