12. If DH = HE, MBG = (9x – 20) and MGC = (5x + 28), find mAB.
1 answer:
Answer:
176degrees
Step-by-step explanation:
Find the diagram attached. From the diagram;
arcGC = = arc BG
5x + 28 = 9x - 20
5x - 9x = -20 28
-4x = -48
x = -48/-4
x = 12
Get <AB
Since <AB = <BC
<BC = arcGC +arc BG
<AB = arcGC+ arc BG
<AB = 5x + 28 + 9x - 20
<AB = 14x + 8
<AB = 14(12) + 8
<AB = 168 + 8
<AB = 176degrees
Hence the arc AB is 176degrees
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Let the measure of angle be 'x'
Since, the measure of the supplement of an angle is 84° less than the measure of the angle.
Therefore, measure of supplement of x = x - 84°
The measure of two supplementary angles is 180 degrees.
So, the measure of angle =
Its supplement = x - 84° = 132° - 84°
= 48°
So, the measure of supplement of angle is 48 degrees.