Home / Digital SAT Math : Lines, angles, and triangles -Practice Questions

Digital SAT Math : Lines, angles, and triangles -Practice Questions

Digital SAT Math : Lines, angles, and triangles -Practice Questions- New Syllabus

DSAT MAth Practice questions – all topics

  • Geometry and Trigonometry Weightage: 15% Questions: 5-7
    • Area and volume
    • Lines, angles, and triangles
    • Right triangles and trigonometry
    • Circles

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Question Easy

In the figure below, lines \( m \) and \( n \) are parallel. What is the value of \( b \)?

Parallel Lines Diagram

A) 40

B) 50

C) 65

D) 80

▶️ Answer/Explanation
Solution

Ans: A

Parallel lines \( m \) and \( n \): 130° + \( a^\circ \) = 180°, so \( a^\circ = 50^\circ \).

In the right triangle (90° at \( l \) and \( m \)), \( a^\circ + b^\circ = 90^\circ \).

\( 50^\circ + b^\circ = 90^\circ \), so \( b^\circ = 40^\circ \).

Question Easy

In a right triangle, the measure of one of the acute angles is 51°. What is the measure, in degrees, of the other acute angle?

A) 6

B) 39

C) 49

D) 51

▶️ Answer/Explanation
Solution

Ans: B

In a right triangle, the acute angles sum to 90°.

Given one angle is 51°, the other is: \( 90^\circ – 51^\circ = 39^\circ \).

Question Easy

Line \( k \) is shown in the \( xy \)-plane. Line \( j \) (not shown) is parallel to line \( k \). What is the slope of line \( j \)?

Line k in xy-plane

A) \( \frac{1}{3} \)

B) 1

C) \( \frac{1}{5} \)

D) 5

▶️ Answer/Explanation
Solution

Ans: C

Line \( k \) passes through points \( (0, 2) \) and \( (5, 3) \).

Slope of \( k \): \( \frac{3 – 2}{5 – 0} = \frac{1}{5} \).

Since \( j \) is parallel to \( k \), its slope is also \( \frac{1}{5} \).

Question Easy

In the figure below, line \( t \) intersects lines \( l \) and \( k \). Which additional piece of information is sufficient to prove that lines \( l \) and \( k \) are parallel?

Lines l, k, and t Intersection

A) \( x > 90 \)

B) \( w < 90 \)

C) \( w = y \)

D) \( y = z \)

▶️ Answer/Explanation
Solution

Ans: D

If \( y = z \), and \( y \) and \( z \) are corresponding or alternate interior angles, then \( l \parallel k \), as equal corresponding or alternate interior angles imply parallelism.

Choice A: Insufficient, \( x > 90 \) doesn’t relate angles on \( l \) and \( k \).

Choice B: Insufficient, \( w < 90 \) doesn’t establish a relationship between \( l \) and \( k \).

Choice C: Insufficient unless \( w \) and \( y \) are corresponding or alternate interior angles, which isn’t guaranteed.

Question Easy

In the \( xy \)-plane above, a dilation with center \( O \) and scale factor 3 transforms triangle \( ABC \) to triangle \( DEF \). Which of the following statements is NOT true?

Triangles ABC and DEF in xy-plane

A) The perimeter of triangle \( DEF \) is 3 times the perimeter of triangle \( ABC \).

B) The measure of angle \( E \) is 3 times the measure of angle \( B \).

C) The length of \( \overline{AB} \) is \( \frac{1}{3} \) the length of \( \overline{DE} \).

D) Angle \( A \) is congruent to angle \( D \)

▶️ Answer/Explanation
Solution

Ans: B

Dilation with scale factor 3 multiplies lengths by 3, but angles remain congruent.

A) TRUE: Perimeter of \( DEF \) is 3 times perimeter of \( ABC \).

B) FALSE: Angle \( E \) is congruent to angle \( B \), not 3 times its measure.

C) TRUE: \( AB = \frac{DE}{3} \) due to the scale factor.

D) TRUE: Angle \( A \) is congruent to angle \( D \).

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