Question

m∠acb=
m∠abc=
m∠bca=
m∠abc=

Explanation:

Problem 3

Step1: Find the value of \(x\)

Since \(\angle DAB = 103^{\circ}\), then \(\angle BAC=180 - 103=77^{\circ}\).
In \(\triangle ABC\), by the angle - sum property of a triangle \(\angle BAC+(3x + 9)+(3x-14)=180\).

$$77+(3x + 9)+(3x-14)=180$$

$$77 + 3x+9+3x - 14=180$$

$$6x+72 = 180$$

$$6x=180 - 72$$

$$6x=108$$

$$x = 18$$

Step2: Calculate \(m\angle ABC\)

Substitute \(x = 18\) into \(\angle ABC=(3x + 9)^{\circ}\)

$$m\angle ABC=3\times18+9=54 + 9=63^{\circ}$$

Step3: Calculate \(m\angle ACB\)

Substitute \(x = 18\) into \(\angle ACB=(3x-14)^{\circ}\)

$$m\angle ACB=3\times18-14=54-14 = 40^{\circ}$$

Step1: Find the value of \(x\)

Since \(\angle CAD = 97^{\circ}\), then \(\angle BAC=180 - 97=83^{\circ}\).
In \(\triangle ABC\), by the angle - sum property of a triangle \(\angle BAC+(14x-1)+(2x + 2)=180\)

$$83+(14x-1)+(2x + 2)=180$$

$$16x+84 = 180$$

$$16x=180 - 84$$

$$16x=96$$

$$x = 6$$

Step2: Calculate \(m\angle ABC\)

Substitute \(x = 6\) into \(\angle ABC=(14x-1)^{\circ}\)

$$m\angle ABC=14\times6-1=84 - 1=83^{\circ}$$

Step3: Calculate \(m\angle BCA\)

Substitute \(x = 6\) into \(\angle BCA=(2x + 2)^{\circ}\)

$$m\angle BCA=2\times6+2=12 + 2=14^{\circ}$$

Answer:

\(m\angle ABC = 63^{\circ}\), \(m\angle ACB=40^{\circ}\)

Problem 4