Question

Question 7 of 9

A
B
Answer here
D
Given that ZBCD and ZBCA form a straight angle, if ZBAC measures 20
degrees and ZABC measures 45 degrees, then the measure of ZBCD is
degrees.

Answer 1

Given information:

m∠BAC=20°

m∠ABC=45°

m∠BCA + m∠BCD = 180°

We are trying to find the m∠BCD

Using the Triangle Sum Theorem, we know the three interior angles in a triangle sum up to 180,° so let’s create an equation:

m∠BAC + m∠ABC + m∠BCA = 180°

Substitute the given information in for the angles:

(20)+(45)+x=180

m∠BCA=x,° x denoting that we do not know the angle measure.

Let’s solve for x:

Add like terms:

65+x=180

Subtract 65 from both sides:

x=180-65

x=115°

So, m∠BCA=115°

Now, we know that:

m∠BCA+m∠BCD=180°

Substitute the information in, and let m∠BCD=y:°

(115)+y=180

Solve for y:

Subtract 115 from both sides:

y=180-115

y=65°

Thus, m∠BCD=65°


This must be true because 65+115=180

Answer: angle BCD is 65°