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Question

Difficulty: HardLines and Angles

Match each geometric angle scenario to its final calculated angle measure.

  • The measure of the larger angle in a supplementary pair where one angle is 20∘20^\circ more than three times the other.140∘140^\circ
  • The measure of the larger angle in a complementary pair where one angle is exactly half the measure of the other.60∘60^\circ
  • The measure of each alternate interior angle formed by parallel lines, expressed as (4x+15)∘(4x + 15)^\circ and (6x−25)∘(6x - 25)^\circ.95∘95^\circ
  • The measure of each vertical angle, expressed as (5y−10)∘(5y - 10)^\circ and (2y+50)∘(2y + 50)^\circ.90∘90^\circ

Answer

The geometric relationships determine the equations: the supplementary pair resolves to 140∘140^\circ, the complementary pair resolves to 60∘60^\circ, the alternate interior angles evaluate to 95∘95^\circ, and the vertical angles evaluate to 90∘90^\circ.
Each correct match correctly identifies the angle relationship, translates it into an accurate algebraic equation, solves for the variable, and completes the final substitution to find the requested angle measure.

Step-by-Step Solution

1
Identify the core geometric relationship for each scenario.
Determine if the angles sum to 180∘180^\circ (supplementary), sum to 90∘90^\circ (complementary), or are mathematically equivalent (alternate interior, vertical).
Recognizing the geometric property is necessary to set up the correct algebraic equation.
2
Translate the text into algebraic equations and solve for the unknown variable.
The variables are calculated as x=40x = 40, x=60x = 60, x=20x = 20, and y=20y = 20 for the four respective scenarios.
Isolating the variable is an intermediate step required to find the specific angle measurements.
3
Calculate the final requested angle measure using the solved variable.
Substitute the variables back into the expressions or apply the logic to find the specific 'larger angle' requested.
The question asks for the final angle measure, not just the isolated variable.

Key Concept

Lines and Angles
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Topics

Lines and Angles

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