Question

what is the value of a?

a = \boxed{\circ}
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solve linear equations: mixed review (36)
angle measures

Explanation:

Step1: Use supplementary angle property

$(a-24^\circ) + (c+25^\circ) = 180^\circ$
Simplify: $a + c + 1^\circ = 180^\circ$ → $a + c = 179^\circ$ → $c = 179^\circ - a$

Step2: Use triangle angle sum property

$(c-41^\circ) + (c-22^\circ) + (a-24^\circ) = 180^\circ$
Simplify: $2c + a - 87^\circ = 180^\circ$ → $2c + a = 267^\circ$

Step3: Substitute $c = 179^\circ - a$

$2(179^\circ - a) + a = 267^\circ$
Expand: $358^\circ - 2a + a = 267^\circ$
Simplify: $358^\circ - a = 267^\circ$

Step4: Solve for $a$

$a = 358^\circ - 267^\circ$

Answer:

$91^\circ$