A cabinetmaker is designing custom geometric inlay patterns using various wood veneers. Ma… — Armed Services Vocational Aptitude Battery (ASVAB)

A cabinetmaker is designing custom geometric inlay patterns using various wood veneers. Match each described angle relationship from the design to the correct pair of angle measures.

Two complementary angles where one angle is $10^\circ$ larger than the other. $40^\circ$ and $50^\circ$
Two vertical angles that have a combined sum of $150^\circ$ . $75^\circ$ and $75^\circ$
A linear pair of angles where one angle is exactly three times the measure of the other. $45^\circ$ and $135^\circ$
Two alternate interior angles formed by a diagonal transversal intersecting parallel wood strips, where one angle measures $110^\circ$ . $110^\circ$ and $110^\circ$

Cevap

Match the complementary angles to 40° and 50°; the vertical angles to 75° and 75°; the linear pair to 45° and 135°; and the alternate interior angles to 110° and 110°.

The correct matches require applying fundamental angle definitions: complementary angles sum to 90 degrees, vertical angles are congruent, a linear pair sums to 180 degrees, and alternate interior angles between parallel lines are congruent.

Adım Adım Çözüm

Calculate the complementary angles.

The angles are

40^\circ

and

50^\circ

Complementary angles sum to exactly

90^\circ

. Set up the equation

x + (x + 10) = 90

, which simplifies to

2x = 80

, so

x = 40

Calculate the vertical angles.

The angles are

75^\circ

and

75^\circ

Vertical angles are always equal in measure. Since they are equal and sum to

150^\circ

, you divide

150^\circ

by 2.

Calculate the linear pair angles.

The angles are

45^\circ

and

135^\circ

Angles in a linear pair sum to

180^\circ

. Set up the equation

x + 3x = 180

, which simplifies to

4x = 180

, so

x = 45

Determine the alternate interior angles.

Both angles are

110^\circ

When parallel lines are intersected by a transversal, alternate interior angles are equal.

Anahtar Kavram

Angle Relationships and Algebraic Substitution

Soru

Cevap

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Anahtar Kavram

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