Geometry ! read the following statements. 1. pqr is acute. 2. pqr is isosceles. 3. pqr is right. which two statements contradict each other? 2 and 3 none of the statements contradict each other. 1 and 2 1 and 3

1 and 3 are contradictory

Step-by-step explanation:

A triangle is acute if all angles are less than 90

A triangle is isosceles if any two angles are congruent.

A triangle is right if one of the angle is 90.

Hence we see that a triangle is acute has all angles less than 90.

So it cannot be simultaneously right triangle.

Thus we find that 1 and 3 are contradictory.

1 and 2 are not contradictory as two acute triangles can be equal and also third is acute.

2 and 3 are not contradictory since when a right triangle has other two angles as 45, 45 then it is isosceles as well as right.

Answer is 1 and 3 are contradictory.

m∠cdf = 43° , m∠gdf = 114°, m∠gde = 23°, m∠edh = 23° , m∠cdh = 157°

step-by-step explanation:

since, it is given that de bisects the angle gdh ⇒ de divides the angle gdh into two equal angles.

⇒ m∠gde = m∠edh

⇒ 8·x   - 1 = 6·x + 5

⇒ x = 3

so, m∠gde = 8·x - 1 = 23°

and m∠edh = 23°

now, it is given ∠cde is an straight angle so, m∠cde = 180°

⇒ m∠cdf + m∠fdg + m∠gde = 180°

⇒ 43° + m∠fdg + 23° = 180°

⇒ m∠fdg = 114°

again, m∠cde = m∠cdh + m∠edh = 180°

m∠cdh + 23° = 180°

⇒ m∠cdh = 157°