Question

two angles are given. m∠g=(2x - 90)°, m∠h=(180 - 2x)°. which statements are true about ∠g and ∠h if both angles are greater than zero? select all that apply. o ∠g and ∠h are complementary angles. o ∠g and ∠h are supplementary angles. o ∠g and ∠h are acute angles. o ∠g and ∠h form a linear - pair. o the sum of ∠g and ∠h is 360.

Explanation:

Step1: Recall angle - relationship definitions

Complementary angles add up to 90°, supplementary angles add up to 180°, a linear - pair of angles add up to 180°, and acute angles are less than 90°.

Step2: Find the sum of ∠g and ∠h

m∠g=(2x - 90)° and m∠h=(180 - 2x)°. Then m∠g + m∠h=(2x - 90)+(180 - 2x)=90°.

Step3: Analyze each option

• Option 1: The sum of ∠g and ∠h is 90°, not 360°. So this is false.
• Option 2: ∠g and ∠h form a linear - pair. A linear - pair has a sum of 180°, but ∠g+∠h = 90°, so this is false.
• Option 3: ∠g and ∠h are acute angles. Let's find the range of x. Since m∠g=(2x - 90)°>0, then 2x>90, x > 45. And m∠h=(180 - 2x)°>0, then 2x<180, x < 90. When x = 50, m∠g=2×50 - 90 = 10° and m∠h=180-2×50 = 80°. But we can't be sure they are always acute. However, we know their sum is 90°.
• Option 4: ∠g and ∠h are supplementary. Supplementary angles sum to 180°, but ∠g+∠h = 90°, so this is false.
• Option 5: ∠g and ∠h are complementary. Since m∠g + m∠h=(2x - 90)+(180 - 2x)=90°, ∠g and ∠h are complementary. This is true.

Answer:

∠g and ∠h are complementary.