△ACD∼△GHD , m∠ADC=23∘ , and m∠C=31∘ . Two similar triangles. The first triangle has vertices DAC. Angle A is an obtuse angle. Th

Question

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△ACD∼△GHD , m∠ADC=23∘ , and m∠C=31∘ . Two similar triangles. The first triangle has vertices DAC. Angle A is an obtuse angle. Th

e second triangle has vertices DGH. Angle G is an obtuse angle. The triangles meet at angle D forming a vertical angle. What is m∠G ? Enter your answer in the box. m∠G = °

Mathematics

1 answer:

iVinArrow [24] · Answer 1 · 2022-04-07T08:49:32+03:00

Answer:

126°

Step-by-step explanation:

The sum of angles in a triangle is 180°. Corresponding angles C and H of the similar triangles have the same measure, so you have ...

... ∠G + ∠H + ∠D = 180°

... ∠G + 31° +23° = 180° . . . . . . . subtract the numbers on the left to find ∠G

... 180° -54° = ∠G = 126°