Questions: Find each angle measure. 12. m ∠ A

Transcript text: Find each angle measure. 12. $\mathrm{m} \angle A$

Solution

Solution Steps

Step 1: Find the value of x.

The angles ∠BCD and ∠BCA are supplementary angles, which means their sum is equal to 180°. Therefore: $m∠BCA + m∠BCD = 180°$ $m∠BCA + 124° = 180°$ $m∠BCA = 180° - 124°$ $m∠BCA = 56°$

The sum of the angles in triangle ABC is 180°. Therefore: $m∠BAC + m∠ABC + m∠BCA = 180°$ $(10x - 5)° + (8x + 3)° + 56° = 180°$ $18x + 54 = 180$ $18x = 180 - 54$ $18x = 126$ $x = \frac{126}{18}$ $x = 7$

Step 2: Find the measure of angle A.

$m∠BAC = (10x - 5)°$ $m∠BAC = (10(7) - 5)°$ $m∠BAC = (70 - 5)°$ $m∠BAC = 65°$