Question

ZRQS, what

of one of the
Use the diagram shown.
re collinear.
5 and LN = 17.
alue of MN?
12. If mZ1 equals (2x + 3) and m23
equals (6x - 17), what is the value
of x? What is mZ1?
13. If m 2 equals (15a + 8) and m23
equals (5a - 8), what is the value
of a?
Cso that
hat is x?

Answer 1

• 12. x = 5, m∠1 = 13°
• 13. a = 9°

Explanation:

12..................................

Given:

• m∠1 = (2x + 3)
• m∠3 = (6x - 17)
• x? m∠1?

Solution:

∠1 and ∠3 are vertical angles.

We know the property that vertical angles are equal:

• 2x + 3 = 6x - 17
• 6x - 2x = 3 + 17
• 4x = 20
• x = 5
• m∠1 = 2*5 + 3 = 13°

13 ..................................

Given

• m ∠ 2 = (15a + 8)
• m ∠ 3 = (5a - 8)
• a = ?

Solution

∠2 and ∠3 are supplementary angles.

We know the property that supplementary angles add up to 180°:

• 15a + 8 + 5a - 8 = 180°
• 20a = 180°
• a = 180°/20
• a = 9°