Question

find the measure of angle a.
21)
23)

Explanation:

Problem 21

Step1: Sum of triangle angles is 180°

$(x+59) + 84 + (x+51) = 180$

Step2: Simplify the equation

$2x + 194 = 180$

Step3: Solve for x

$2x = -14 \Rightarrow x = -7$

Step4: Calculate angle A

$x + 51 = -7 + 51 = 44$

Step1: Linear pair angle

Adjacent angle to 130° is $180 - 130 = 50°$

Step2: Vertical angles are equal

Opposite angle to 50° is 50°, so the triangle has angles $3x-6$, $8x+4$, 50°

Step3: Sum of triangle angles is 180°

$(3x-6) + (8x+4) + 50 = 180$

Step4: Simplify the equation

$11x + 48 = 180$

Step5: Solve for x

$11x = 132 \Rightarrow x = 12$

Step6: Calculate angle A

$3x - 6 = 3(12) - 6 = 30$

Answer:

44°

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Problem 23