Question

If the measure of angle 2=a+15 and the measure of angle 3=a+35, find a if HL is perpendicular to HJ

Answer 1

The value of a if HL is perpendicular to HJ is 20

How to determine the value

From the information given, we have that;

• HL = angle 2 = a + 15
• HJ = angle 3 = HJ

It is important to note that perpendicular lines always intersect each other and the angle between perpendicular lines is equivalent to 90 degrees.

Then, we have that;

Angle 2 + angle 3 =  90 degrees

Substitute the values

a + 15 + a + 35 = 90

collect like terms

2a + 50 = 90

2a = 90 - 50

subtract like terms

2a = 40

Make 'a' the subject

Divide both sides by 2

2a/2 = 40/2

a = 20

Thus, the value of a if HL is perpendicular to HJ is 20

Learn more about perpendicular lines here:

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