Question
Select all the statements that are true about Delta MKH If mangle M=38^circ then mangle DHM=52^circ If mangle M=38^circ then mangle K=52^circ If mangle K=47 and mangle M=21^circ then mangle MHK=112^circ If mangle K=63^circ and mangle M=17^circ then mangle MHK=80^circ If mangle M=55^circ and mangle KHM=103^circ then mangle K=158^circ
Answer
4.3
(266 Votes)
Valerie
Elite · Tutor for 8 years
Answer
Let's evaluate each statement one by one:1. If
, then
.Since
is a right triangle with
being the right angle, the sum of the angles in a triangle is
. Therefore,
. Given
and
(since it's a right angle), we can find
as follows:\(m \angle H = 180^{\circ} - (m \angle M + m \angle K) = 180^{\circ} - (38^{\circ} + 90^{\circ}) = 180^{\circ} - 128^{\circ} = 52^{\circ}\).Therefore,
. This statement is true.2. If
, then
.This statement is false because
is a right angle, which means
, not
.3. If
and
, then
.This statement cannot be true because
is a right angle, which means
. The given condition
is incorrect for a right triangle. Therefore, any conclusion drawn from this incorrect information is invalid.4. If
and
, then
.Again, this statement is incorrect because
is a right angle, which means
. The given condition
is incorrect for a right triangle.5. If
and
, then
.This statement is false because
is a right angle, which means
. Additionally, the sum of the angles in a triangle cannot exceed
, so
cannot be
.In conclusion, the only true statement is the first one:If
, then
.